Question

Find the area of an isosceles right angled triangle in which its hypotenuse is 20cm.

Answer 1

h²=p²+b²
as it is isosceles triangle
h²=b²+b²
h²=2b²
so,
b=√(h²/2)
b=√20²/2
b=20/√2
so,
area=1/2×b×p=1/2×20/√2×20/√2=100

Answer 2

Hypotenuse=20 cm
According to Pythagoras theorem,
Hypotenuse ²=side²+side²
Let hypotenuse=a
Base=b
Height=c
In an isosceles right angled triangle,
The other two sides are equal.
So,base=height=b

Apply Pythagoras theorem,
a²=b²+b²
a²=2b²
b=√(a²/2)
b=√(20²/2)
b=20/√2

Area of isosceles right angled triangle=1/2×b×h
=1/2×20/√2×20/√2
=1/2×400/2
=400/4
=100 cm²

Hope it helps