Maharashtra State BoardSSC (English Medium) 7th Standard

Find the Pythagorean Triplets from Among the Following Set of Numbers. 3, 4, 5 - Mathematics

Advertisements
Advertisements
Sum

Find the Pythagorean triplets from among the following set of numbers.

3, 4, 5

Advertisements

Solution

It is known that, if in a triplet of natural numbers, the square of the biggest number is equal to the sum of the squares of the other two numbers, then the three numbers form a Pythagorean triplet.

The given set of numbers is (3, 4, 5).
The biggest number among the given set is 5.
52 = 25; 42 = 16; 32 = 9
Now, 16 + 9 = 25
∴ 42 + 32 = 52
Thus, (3, 4, 5) form a Pythagorean triplet.

  Is there an error in this question or solution?
Chapter 13: Pythagoras’ Theorem - Practice Set 49 [Page 90]

APPEARS IN

Balbharati Mathematics 7th Standard Maharashtra State Board
Chapter 13 Pythagoras’ Theorem
Practice Set 49 | Q 1.1 | Page 90

RELATED QUESTIONS

If the sides of a triangle are 6 cm, 8 cm and 10 cm, respectively, then determine whether the triangle is a right angle triangle or not.


A man goes 10 m due east and then 24 m due north. Find the distance from the starting point


In a ∆ABC, AD ⊥ BC and AD2 = BC × CD. Prove ∆ABC is a right triangle


ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2 


ABC is an equilateral triangle of side 2a. Find each of its altitudes.


In the given figure, ABC is a triangle in which ∠ABC> 90° and AD ⊥ CB produced. Prove that AC2 = AB2 + BC2 + 2BC.BD.


Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, ho much string does she have out (see Figure)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?


Which of the following can be the sides of a right triangle?

2 cm, 2 cm, 5 cm

In the case of right-angled triangles, identify the right angles.


Identify, with reason, if the following is a Pythagorean triplet.
(4, 9, 12)


Identify, with reason, if the following is a Pythagorean triplet.
(5, 12, 13)


Identify, with reason, if the following is a Pythagorean triplet.
(10, 24, 27)


In the given figure, M is the midpoint of QR. ∠PRQ = 90°. Prove that, PQ= 4PM– 3PR2.


Walls of two buildings on either side of a street are parellel to each other. A ladder 5.8 m long is placed on the street such that its top just reaches the window of a building at the height of 4 m. On turning the ladder over to the other side of the street , its top touches the window of the other building at a height 4.2 m. Find the width of the street.


In ∆PQR, point S is the midpoint of side QR. If PQ = 11, PR = 17, PS = 13, find QR.


In ∆ABC, AB = 10, AC = 7, BC = 9, then find the length of the median drawn from point C to side AB.


Some question and their alternative answer are given. Select the correct alternative.

If a, b, and c are sides of a triangle and a+ b= c2, name the type of triangle.


Find the length of the hypotenuse of a right angled triangle if remaining sides are 9 cm and 12 cm.


In a trapezium ABCD, seg AB || seg DC seg BD ⊥ seg AD, seg AC ⊥ seg BC, If AD = 15, BC = 15 and AB = 25. Find A(▢ABCD)


A ladder 13 m long rests against a vertical wall. If the foot of the ladder is 5 m from the foot of the wall, find the distance of the other end of the ladder from the ground.


In the figure: ∠PSQ = 90o, PQ = 10 cm, QS = 6 cm and RQ = 9 cm. Calculate the length of PR.


In triangle ABC, given below, AB = 8 cm, BC = 6 cm and AC = 3 cm. Calculate the length of OC.



In the figure, given below, AD ⊥ BC.
Prove that: c2 = a2 + b2 - 2ax.


In an isosceles triangle ABC; AB = AC and D is the point on BC produced.
Prove that: AD2 = AC2 + BD.CD.


O is any point inside a rectangle ABCD.
Prove that: OB2 + OD2 = OC2 + OA2.


In a quadrilateral ABCD, ∠B = 90° and ∠D = 90°.
Prove that: 2AC2 - AB2 = BC2 + CD2 + DA2


In triangle ABC, ∠B = 90o and D is the mid-point of BC.
Prove that: AC2 = AD2 + 3CD2.


If the angles of a triangle are 30°, 60°, and 90°, then shown that the side opposite to 30° is half of the hypotenuse, and the side opposite to 60° is `sqrt(3)/2` times of the hypotenuse.


Choose the correct alternative: 

In right-angled triangle PQR, if hypotenuse PR = 12 and PQ = 6, then what is the measure of ∠P? 


Find the length of diagonal of the square whose side is 8 cm.


Find the side of the square whose diagonal is `16sqrt(2)` cm.


Triangle ABC is right-angled at vertex A. Calculate the length of BC, if AB = 18 cm and AC = 24 cm.


Triangle XYZ is right-angled at vertex Z. Calculate the length of YZ, if XY = 13 cm and XZ = 12 cm.


Triangle PQR is right-angled at vertex R. Calculate the length of PR, if: PQ = 34 cm and QR = 33.6 cm.


In triangle PQR, angle Q = 90°, find: PR, if PQ = 8 cm and QR = 6 cm


In triangle PQR, angle Q = 90°, find: PQ, if PR = 34 cm and QR = 30 cm


In the given figure, angle ACB = 90° = angle ACD. If AB = 10 m, BC = 6 cm and AD = 17 cm, find :
(i) AC
(ii) CD


In the given figure, AD = 13 cm, BC = 12 cm, AB = 3 cm and angle ACD = angle ABC = 90°. Find the length of DC.


A ladder, 6.5 m long, rests against a vertical wall. If the foot of the ladder is 2.5 m from the foot of the wall, find up to how much height does the ladder reach?


A boy first goes 5 m due north and then 12 m due east. Find the distance between the initial and the final position of the boy.


Use the information given in the figure to find the length AD.


In the right-angled ∆PQR, ∠ P = 90°. If l(PQ) = 24 cm and l(PR) = 10 cm, find the length of seg QR.


In the right-angled ∆LMN, ∠M = 90°. If l(LM) = 12 cm and l(LN) = 20 cm, find the length of seg MN.


Find the Pythagorean triplet from among the following set of numbers.

4, 5, 6


Find the Pythagorean triplet from among the following set of numbers.

4, 7, 8


The sides of the triangle are given below. Find out which one is the right-angled triangle?

8, 15, 17


The sides of the triangle are given below. Find out which one is the right-angled triangle?

11, 12, 15


The sides of the triangle are given below. Find out which one is the right-angled triangle?

11, 60, 61


The sides of the triangle are given below. Find out which one is the right-angled triangle?

1.5, 1.6, 1.7


The sides of the triangle are given below. Find out which one is the right-angled triangle?

40, 20, 30


From the given figure, find the length of hypotenuse AC and the perimeter of ∆ABC.


A ladder 25m long reaches a window of a building 20m above the ground. Determine the distance of the foot of the ladder from the building.


The foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground. If the ladder is shifted in such a way that its foot is 8m away from the wall to what height does its tip reach?


Two poles of height 9m and 14m stand on a plane ground. If the distance between their 12m, find the distance between their tops.


The length of the diagonals of rhombus are 24cm and 10cm. Find each side of the rhombus.


In an equilateral triangle ABC, the side BC is trisected at D. Prove that 9 AD2 = 7 AB2.


From a point O in the interior of aΔABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that: AF2 + BD2 + CE= OA2 + OB2 + OC2 - OD2 - OE2 - OF2


In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 = AD2 + BC x DE + `(1)/(4)"BC"^2`


In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 - AB2 = 2BC x ED


In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that: 9AQ2 = 9AC2 + 4BC2 


In a right-angled triangle PQR, right-angled at Q, S and T are points on PQ and QR respectively such as PT = SR = 13 cm, QT = 5 cm and PS = TR. Find the length of PQ and PS.


∆ABC is right-angled at C. If AC = 5 cm and BC = 12 cm. find the length of AB.


A man goes 18 m due east and then 24 m due north. Find the distance of his current position from the starting point?


There are two paths that one can choose to go from Sarah’s house to James's house. One way is to take C street, and the other way requires to take B street and then A street. How much shorter is the direct path along C street?


To get from point A to point B you must avoid walking through a pond. You must walk 34 m south and 41 m east. To the nearest meter, how many meters would be saved if it were possible to make a way through the pond?


The perpendicular PS on the base QR of a ∆PQR intersects QR at S, such that QS = 3 SR. Prove that 2PQ2 = 2PR2 + QR2 


Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels at a speed of `(20 "km")/"hr"` and the second train travels at `(30 "km")/"hr"`. After 2 hours, what is the distance between them?


If in a ΔPQR, PR2 = PQ2 + QR2, then the right angle of ∆PQR is at the vertex ________


If ‘l‘ and ‘m’ are the legs and ‘n’ is the hypotenuse of a right angled triangle then, l2 = ________


In a right angled triangle, the hypotenuse is the greatest side


Find the unknown side in the following triangles


Find the unknown side in the following triangles


Find the unknown side in the following triangles


An isosceles triangle has equal sides each 13 cm and a base 24 cm in length. Find its height


In triangle ABC, line I, is a perpendicular bisector of BC.
If BC = 12 cm, SM = 8 cm, find CS


The hypotenuse of a right angled triangle of sides 12 cm and 16 cm is __________


In the figure, find AR


Choose the correct alternative:

If length of sides of a triangle are a, b, c and a2 + b2 = c2, then which type of triangle it is?


From given figure, In ∆ABC, If AC = 12 cm. then AB =?


Activity: From given figure, In ∆ABC, ∠ABC = 90°, ∠ACB = 30°

∴ ∠BAC = `square`

∴ ∆ABC is 30° – 60° – 90° triangle

∴ In ∆ABC by property of 30° – 60° – 90° triangle.

∴ AB = `1/2` AC and `square` = `sqrt(3)/2` AC

∴ `square` = `1/2 xx 12` and BC = `sqrt(3)/2 xx 12`

∴ `square` = 6 and BC = `6sqrt(3)`


In the given figure, ∠T and ∠B are right angles. If the length of AT, BC and AS (in centimeters) are 15, 16, and 17 respectively, then the length of TC (in centimeters) is ______.


The perimeters of two similar triangles ABC and PQR are 60 cm and 36 cm respectively. If PQ = 9 cm, then AB equals ______.


If ΔABC ~ ΔPQR, `("ar" triangle "ABC")/("ar" triangle "PQR") = 9/4` and AB = 18 cm, then the length of PQ is ______.


Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangles drawn on the other two sides of the triangle.


In an isosceles triangle PQR, the length of equal sides PQ and PR is 13 cm and base QR is 10 cm. Find the length of perpendicular bisector drawn from vertex P to side QR.


The top of a broken tree touches the ground at a distance of 12 m from its base. If the tree is broken at a height of 5 m from the ground then the actual height of the tree is ______.


In a right-angled triangle ABC, if angle B = 90°, BC = 3 cm and AC = 5 cm, then the length of side AB is ______.


The longest side of a right angled triangle is called its ______.


Two squares having same perimeter are congruent.


If two legs of a right triangle are equal to two legs of another right triangle, then the right triangles are congruent.


Jayanti takes shortest route to her home by walking diagonally across a rectangular park. The park measures 60 metres × 80 metres. How much shorter is the route across the park than the route around its edges?


Points A and B are on the opposite edges of a pond as shown in figure. To find the distance between the two points, the surveyor makes a right-angled triangle as shown. Find the distance AB.


Two poles of 10 m and 15 m stand upright on a plane ground. If the distance between the tops is 13 m, find the distance between their feet.


Share
Notifications



      Forgot password?
Use app×