The length of the hypotenuse of an isosceles right-angled triangle is 24. Find the area of the triangle.

Given:

The length of the hypotenuse of an isosceles right-angled triangle is 24.

To do:

We have to find the area of the triangle.

Solution:

Let the other two sides be $x$.

In the right-angled triangle, by Pythagoras theorem,

$x^2 + x^2 = 24^2$

$2x^2= 576$

$x^2 = 288$

$x=\sqrt{288}$

$x = 12\sqrt2$

Therefore,

Area of the triangle $= \frac{1}{2} \times$ base $\times$ height

Area $= \frac{1}{2}\times12\sqrt2\times12\sqrt2$

$=144\ cm^2$

The area of the triangle is $144\ cm^2$.

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Updated on: 10-Oct-2022

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