Tamil Nadu Board of Secondary EducationSSLC (English Medium) (5 to 8) Class 8

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

Advertisements
Advertisements
Sum

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

Advertisements

Solution


In an isosceles triangle the altitude dives its base into two equal parts.

Now in the figure, ∆ABC is an isosceles triangle with AD as its height

In the figure, AD is the altitude and ∆ABD is a right triangle.

By Pythagoras theorem,

AB2 = AD2 + BD2

⇒ AD2 = AB2 – BD2

= 132 – 122 = 169 – 144 = 25

AD2 = 25 = 52

Height: AD = 5 cm

  Is there an error in this question or solution?
Chapter 5: Geometry - Exercise 5.2 [Page 178]

APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 8th Mathematics Answers Guide
Chapter 5 Geometry
Exercise 5.2 | Q 5 | Page 178

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.


Sides of triangle are given below. Determine it is a right triangle or not? In case of a right triangle, write the length of its hypotenuse. 50 cm, 80 cm, 100 cm

 


 In Figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that AD2 = BD × CD


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


In the following figure, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Show that

(i) OA2 + OB2 + OC2 − OD2 − OE2 − OF2 = AF2 + BD2 + CE2

(ii) AF2 + BD2 + CE= AE2 + CD2 + BF2


In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.


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?


ABC is a triangle right angled at C. If AB = 25 cm and AC = 7 cm, find BC.


A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.


A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.


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.


Prove that the points A(0, −1), B(−2, 3), C(6, 7) and D(8, 3) are the vertices of a rectangle ABCD?


Identify, with reason, if the following is a Pythagorean triplet.
(3, 5, 4)


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


Identify, with reason, if the following is a Pythagorean triplet.
(11, 60, 61)


Find the length diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.


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


In the given figure, point T is in the interior of rectangle PQRS, Prove that, TS+ TQ= TP+ TR(As shown in the figure, draw seg AB || side SR and A-T-B)


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)


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.


If the sides of the triangle are in the ratio 1: `sqrt2`: 1, show that is a right-angled triangle.


In triangle ABC, AB = AC = x, BC = 10 cm and the area of the triangle is 60 cm2.
Find x.


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


ABC is a triangle, right-angled at B. M is a point on BC.
Prove that: AM2 + BC2 = AC2 + BM2.


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


In the following Figure ∠ACB= 90° and CD ⊥ AB, prove that  CD2  = BD × AD


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.


Prove that (1 + cot A - cosec A ) (1 + tan A + sec A) = 2


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


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


The sides of a certain triangle is given below. Find, which of them is right-triangle

16 cm, 20 cm, and 12 cm


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


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


Show that the triangle ABC is a right-angled triangle; if: AB = 9 cm, BC = 40 cm and AC = 41 cm


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.


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.


The top of a ladder of length 15 m reaches a window 9 m above the ground. What is the distance between the base of the wall and that of the ladder?


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

2, 4, 5


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?

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


Find the length of the perpendicular of a triangle whose base is 5cm and the hypotenuse is 13cm. Also, find its area.


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


A ladder 15m long reaches a window which is 9m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to other side of the street to reach a window 12m high. Find the width of the street.


In ΔABC, AD is perpendicular to BC. Prove that: AB2 + CD2 = AC2 + BD2


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`


A point OI in the interior of a rectangle ABCD is joined with each of the vertices A, B, C and D. Prove that  OB2 + OD2 = OC2 + OA2


AD is perpendicular to the side BC of an equilateral ΔABC. Prove that 4AD2 = 3AB2.


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


In a right-angled triangle ABC,ABC = 90°, AC = 10 cm, BC = 6 cm and BC produced to D such CD = 9 cm. Find the length of AD.


In a square PQRS of side 5 cm, A, B, C and D are points on sides PQ, QR, RS and SP respectively such as PA = PD = RB = RC = 2 cm. Prove that ABCD is a rectangle. Also, find the area and perimeter of the rectangle.


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 ‘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


Find the distance between the helicopter and the ship


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 =?


In a right angled triangle, if length of hypotenuse is 25 cm and height is 7 cm, then what is the length of its base?


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)`


If S is a point on side PQ of a ΔPQR such that PS = QS = RS, then ______.


In an equilateral triangle PQR, prove that PS2 = 3(QS)2.


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 ______.


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?


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×