Question

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

Answer 1

half ×base ×height =200 cm
base ×height =200×2 =400
since base and height are equal
base=height=root 400=20
20 square +20 square=hypotenuse
800=hypotenuse square
hypotenuse =root 800

Answer 2

Answer:

The length of hypotenuse is $20\sqrt2$

Step-by-step explanation:

Let the two equal sides of the isosceles right triangle is x and the hypotenuse is y.

The area of a triangle is given by

$A=\frac{1}{2}x\cdotx\\\\200=\frac{1}{2}x^2\\\\x^2=400\\\\x=20$

Hence, two equal sides are 20 cm each.

From Pythagorean theorem,

$x^2+x^2=y^2\\\\20^2+20^2=y^2\\\\y^2=400+400\\\\y^2=800\\\\y=\sqrt{800}\\\\y=20\sqrt2$

The length of hypotenuse is $20\sqrt2$