An isosceles right triangle has area 8 cm². The length of its hypotenuse is
a. √32 cm
b. √16 cm
c. √48 cm
d. √24 cm

Solution:

Given, an isosceles right triangle has area 8 cm².

We have to find the length of its hypotenuse.

We know that in an isosceles triangle two sides are of equal length.

Here, AB = BC

AC is the hypotenuse

Area of triangle = 1/2 × base × height

8 = 1/2 × AB × BC

8 = 1/2 × AB²

AB² = 8 × 2

AB² = 16

Taking square root,

AB = 4 cm

In triangle ABC,

By using Pythagorean theorem,

AB² + BC² = AC²

(4)² + (4)² = AC²

AC² = 16 + 16

AC² = 32

Taking square root,

AC = √32 cm

Therefore, the length of the hypotenuse is √32 cm.

✦ Try This: An isosceles right triangle has area 36 cm². The length of its hypotenuse is

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 12

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NCERT Exemplar Class 9 Maths Exercise 12.1 Problem 1

An isosceles right triangle has area 8 cm². The length of its hypotenuse is a. √32 cm, b. √16 cm, c. √48 cm, d. √24 cm

Summary:

An isosceles triangle is defined as a triangle that has two sides of equal measure. An isosceles right triangle has area 8 cm² . The length of its hypotenuse is √32 cm

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