Question

area of an isosceles right triangle is 24.5 cm^2;length of its hypotenuse is​

Answer 1

ANSWER:

Given:

• Area of an isosceles triangle = 24.5 sq cm.

To Find:

• Length of hypotenuse

Solution:

We are given that,

$\implies\rm{Area\:of\:triangle=24.5cm^2}$

We know that,

$\implies\rm{Area\:of\:triangle=\dfrac{1}{2}\times base\times height}$

So,

$\implies\rm{ \dfrac{1}{2}\times base\times height =24.5cm^2}$

Transposing 2 to RHS,

$\implies\rm{base\times height =49}$

As the triangle is an isosceles one, base and height are same.

So,

$\implies\rm{base\times base =49}$

$\implies\rm{base^2 =49}$

Taking square root,

$\implies\rm{base =7}$

Therefore,

$\implies\rm{base=height=7cm}$

Now, we know that, by Pythagoras Theorem,

$\implies\rm{Hypotenuse=\sqrt{Base^2+Height^2}}$

So,

$\implies\rm{Hypotenuse=\sqrt{Base^2+Height^2}}$

$\implies\rm{Hypotenuse=\sqrt{7^2+7^2}}$

$\implies\rm{Hypotenuse=\sqrt{2(7^2)}}$

$\implies\bf{Hypotenuse=7\sqrt{2}}$

Therefore, the length of hypotenuse is 7√2 cm.