Question

an isosceles right triangle has area 200 CM square find the length of its hypotenuse

Answer 1

Let the sides be x
Then
Area of triangle = 1/2× b ×h
200 = 1/2×X×X
400= X^2
X = 20

Hypo^2 = base^2 + altitude^2

= 400+400
Hypo = √ 800
= 20√2 ans

I hope it help you

Answer 2

Hey there !

Solution:

Given that, it is a right angled isosceles triangle. So it means that the sides other than hypotenuse are equal in measure.

So let the side be denoted as 'x'

Now Area of triangle is given as 200 cm²

So Area of triangle = 1/2 * Base * Height

=> Area = 1/2 * x * x

=> Area = 1/2 * x² = x²/2

=> x²/2 = 200 cm²

=> x² = 200 × 2 = 400 cm²

=> x = √400 = 20 cm

So Applying Pythagoras Theorem we get,

=> x² + x² = Hypotenuse²

=> 20² + 20² = Hypotenuse²

=> 400 + 400 = Hypotenuse²

=> 800 = Hypotenuse²

=> Hypotenuse = √800 = 20√2 cm

Hence the side of the hypotenuse is 20√2 cm

Hope my answer helped !