Question

an isosceles right angled triangle has an area 8 cm square find length of its hyptenuse

Answer 1

Hey Friend,

Since the triangle is isosceles triangle,
Let the perpendicular and the base be 'x' cm.

According to given,
Area = 8 cm^2
1/2 x h x b = 8 cm^2
x^2 = 16
x = 4 cm 

Therefore, the sides are 4 cm.

Now, Applying Pythagoras theorem,
hypotenuse^2 = height^2 + base^2
hypotenuse^2 = 4^2 + 4^2
hypotenuse^2 = 16 + 16
hypotenuse = $\sqrt{32}$
hypotenuse = 4 $\sqrt{2}$
hypotenuse = 4 x 1.414
hypotenuse = 5.656 cm

Therefore, the length of hypotenuse is 5.656 cm or 4 $\sqrt{2}$ cm

Hope it helps!

Answer 2

Hola Friend ✋✋✋

It is a isoceles triangle , so base and Height will be equal

b = h

Area of Triangle = ½ × b × h

8 = ½ × b²

b² = 16

b = 4 cm

By Pythagoras theorem....

( Hypotenuse ) ² = ( Base ) ² + ( Height ) ²

( Hypotenuse ) ² = 4² + 4²

( Hypotenuse ) ² = 32

Hypotenuse = √32 = 4√2 cm

If you need in decimal...

4√2 = 4 × 1.41 = 5.64 cm

Hope it helps