The length of the hypotenuse of an isosceles right-angled triangle is $ 20 . $ Find the perimeter and area of the triangle.

Given:

The length of the hypotenuse of an isosceles right-angled triangle is 20.

To do:

We have to find the perimeter and area of the triangle.

Solution:

Let the other two sides be $x$.

In the right-angled triangle, by Pythagoras theorem,

$x^2 + x^2 = 20^2$

$2x^2= 400$

$x^2 = 200$

$x=\sqrt{200}$

$x = 10\sqrt2$

Therefore,

Perimeter of the triangle $=3x$

$=3\times10\sqrt2$

$=30\sqrt2\ cm$

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

Area $= \frac{1}{2}\times10\sqrt2\times10\sqrt2$

$=100\ cm^2$

The perimeter of the triangle is $30\sqrt2\ cm$ and the area of the triangle is $100\ cm^2$. 

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Updated on: 10-Oct-2022

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