Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10

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 mak - Mathematics

Advertisements
Advertisements
Sum

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?

Advertisements

Solution

In the right ∆ABC,

By Pythagoras theorem

AC2 = AB2 + BC2 

= 342 + 412

= 1156 + 1681

= 2837

AC = `sqrt(2837)`

= 53.26 m

A one must walk (34m + 41m) 75m to reach C.

The difference in Distance = 75 – 53.26

= 21.74 m

  Is there an error in this question or solution?
Chapter 4: Geometry - Exercise 4.3 [Page 187]

APPEARS IN

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.


In a right triangle ABC, right-angled at B, BC = 12 cm and AB = 5 cm. The radius of the circle inscribed in the triangle (in cm) is
(A) 4
(B) 3
(C) 2
(D) 1


ABCD is a rhombus. Prove that AB2 + BC2 + CD2 + DA2= AC2 + BD2


Sides of triangles are given below. Determine it is a right triangles? In case of a right triangle, write the length of its hypotenuse. 3 cm, 8 cm, 6 cm


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


Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals


A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?


In the given figure, AD is a median of a triangle ABC and AM ⊥ BC. Prove that:

`"AC"^2 = "AD"^2 + "BC"."DM" + (("BC")/2)^2`


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

1.5 cm, 2 cm, 2.5 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.
(11, 60, 61)


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


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


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.


Pranali and Prasad started walking to the East and to the North respectively, from the same point and at the same speed. After 2 hours distance between them was \[15\sqrt{2}\]

 km. Find their speed per hour.

 


In ∆ABC, seg AD ⊥ seg BC, DB = 3CD.

Prove that: 2AB= 2AC+ BC2


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)


Digonals of parallelogram WXYZ intersect at point O. If OY =5, find WY.


In ΔMNP, ∠MNP = 90˚, seg NQ ⊥ seg MP, MQ = 9, QP = 4, find NQ.


In right angle ΔABC, if ∠B = 90°, AB = 6, BC = 8, then find AC.


In ΔABC,  Find the sides of the triangle, if:

  1. AB =  ( x - 3 ) cm, BC = ( x + 4 ) cm and AC = ( x + 6 ) cm
  2. AB = x cm, BC = ( 4x + 4 ) cm and AC = ( 4x + 5) cm

The given figure shows a quadrilateral ABCD in which AD = 13 cm, DC = 12 cm, BC = 3 cm and ∠ABD = ∠BCD = 90o. Calculate the length of AB.


AD is drawn perpendicular to base BC of an equilateral triangle ABC. Given BC = 10 cm, find the length of AD, correct to 1 place of decimal.


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


Diagonals of rhombus ABCD intersect each other at point O.

Prove that: OA2 + OC2 = 2AD2 - `"BD"^2/2`


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


In a rectangle ABCD,
prove that: AC2 + BD2 = AB2 + BC2 + CD2 + DA2.


M andN are the mid-points of the sides QR and PQ respectively of a PQR, right-angled at Q.
Prove that:
(i) PM2 + RN2 = 5 MN2
(ii) 4 PM2 = 4 PQ2 + QR2
(iii) 4 RN2 = PQ2 + 4 QR2(iv) 4 (PM2 + RN2) = 5 PR2


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.


Find the value of (sin2 33 + sin2 57°)


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.


In the given figure, angle BAC = 90°, AC = 400 m, and AB = 300 m. Find the length of BC.


In the given figure, angle ACP = ∠BDP = 90°, AC = 12 m, BD = 9 m and PA= PB = 15 m. Find:
(i) CP
(ii) PD
(iii) CD


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, angle ADB = 90°, AC = AB = 26 cm and BD = DC. If the length of AD = 24 cm; find the length of BC.


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


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


In the figure below, find the value of 'x'.


In the figure below, find the value of 'x'.


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.

2, 6, 7


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?

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


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


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?


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


Each side of rhombus is 10cm. If one of its diagonals is 16cm, find the length of the other diagonals.


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: AB2 = AD2 - BC x CE + `(1)/(4)"BC"^2`


In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 + AC2 = 2(AD2 + CD2)


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: 9BP2 = 9BC2 + 4AC2


In the given figure, PQ = `"RS"/(3)` = 8cm, 3ST = 4QT = 48cm.
SHow that ∠RTP = 90°.


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?


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 ‘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 distance between the helicopter and the ship


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 __________


Find the length of the support cable required to support the tower with the floor


Rithika buys an LED TV which has a 25 inches screen. If its height is 7 inches, how wide is the screen? Her TV cabinet is 20 inches wide. Will the TV fit into the cabinet? Give reason


In the figure, find AR


From the given figure, in ∆ABQ, if AQ = 8 cm, then AB =?


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


In the given figure, AD is a median of a triangle ABC and AM ⊥ BC. Prove that:

(i) `"AC"^2 = "AD"^2 + "BC"."DM" + (("BC")/2)^2`

(ii) `"AB"^2 = "AD"^2 - "BC"."DM" + (("BC")/2)^2`

(iii) `"AC"^2 + "AB"^2 = 2"AD"^2 + 1/2"BC"^2`


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.


In the adjoining figure, a tangent is drawn to a circle of radius 4 cm and centre C, at the point S. Find the length of the tangent ST, if CT = 10 cm.


The perimeter of the rectangle whose length is 60 cm and a diagonal is 61 cm 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 ______.


Two squares are congruent, if they have same ______.


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?


Height of a pole is 8 m. Find the length of rope tied with its top from a point on the ground at a distance of 6 m from its bottom.


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×