Question

An isosceles right triangle has area 8 cm square . Find the length of its hypotenuse.

Answer 1

Both the perpendicular and base are equal in length.

So Area of triangle = 1/2 x b x h

Let b = h = y

1/2 x y x y = 8
y² = 16
y = 4

So Perpendicular = Base = 4 cm

Now by Pythagoras theorem,
4² + 4² = √ 16+ 16 = √32 = 4√2 cm

So required hypotenuse = 4√2 cm

Answer 2

In an isosceles triangle two sides are equal.
Here the the base and the perpendicular of the triangle are equal in length.

Area of triangle = 8cm^2

8cm^2 = 1/2 × b × h
Put b & h as X
16 = x^2
X = 4 cm

So​, the length of base and perpendicular are 4cm.

H^2 = B^2 + P^2
( H is hypotenuse,B is base & P is perpendicular)

H^2 = 4^4 + 4^2
H^2 = 16 + 16
H = √32
H = 4√2
H = 5.65cm
H = 5.7cm


Hope it helps..............