Question

if the area of an isosceles triangle is 8cm².find its hypotenuse?
urgent need​

Answer 1

Answer:

We know

Area of an Isosceles Triangle=

$\frac{1}{2} \times b \times h$

where

b= base

h= height

here given it's isosceles, hence base=height

as they can't be equal to Hypotenuse, because Hypotenuse is the longest side of a right angled triangle.

So let the base and height be x each

as they are equal

that is

$\frac{1}{2} \times x \times x = 8 \\ \frac{ {x}^{2} }{2} = 8 \\ {x}^{2} = 2 \times 8 = 16 \\x = \sqrt{16} \\ x = 4$

therefore the base and height= 4 cm each

Let's verify it

$\frac{1}{2} \times 4 \times 4 = 8 \\ \frac{1}{2} \times 16 = 8 \\ \frac{16}{2} = 8 \\ 8 = 8$

L.H.S=R.H.S

But we've to find Hypotenuse

We know

According to Pythagorean Theorem

Hypotenuse²=base²+altitude

Hypotenuse²=4²+4²

H²=16+16

H²=32

H=√32

H=4√2

Therefore the length of the Hypotenuse is 4√2 cm