Advertisements
Advertisements
Question
Find the length of the hypotenuse of a triangle whose other two sides are 24cm and 7cm.
Advertisements
Solution
The two sides (excluding hypotenuse) of a right-angled triangle are given as 24cm and 7cm
(hypotenuse)2 = (24cm)2 + (7cm)2
(hypotenuse)2 = 576cm2 + 49cm2
(hypotenuse)2 = 625cm2
(hypotenuse)2 = (25cm)2
Thus, the length of the hypotenuse of the triangle is 25cm.
APPEARS IN
RELATED QUESTIONS
In triangle ABC, ∠C=90°. Let BC= a, CA= b, AB= c and let 'p' be the length of the perpendicular from 'C' on AB, prove that:
1. cp = ab
2. `1/p^2=1/a^2+1/b^2`
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. 13 cm, 12 cm, 5 cm
D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE2 + BD2 = AB2 + DE2
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.
(3, 5, 4)
Identify, with reason, if the following is a Pythagorean triplet.
(4, 9, 12)
In figure AB = BC and AD is perpendicular to CD.
Prove that: AC2 = 2BC. DC.
In the following Figure ∠ACB= 90° and CD ⊥ AB, prove that CD2 = BD × AD
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?
In the right-angled ∆PQR, ∠ P = 90°. If l(PQ) = 24 cm and l(PR) = 10 cm, find the length of seg QR.
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?
40, 20, 30
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.
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?
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, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 + AC2 = 2(AD2 + CD2)
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.
Find the unknown side in the following triangles
Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is ______.
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.
