Question

if the area of an isosceles right angled triangle is 8cm² then what is the perimeter of the triangle

Answer 1

Hi !

base = b 
altitude = h

A.T.Q.,

b = a

we have to find hypotenuse

We know that,

Area of triangle = 1/2bh
8 = 1/2bh

but , b = h 

8 = 1/2b*b
8 = 1/2b²

b² = 8*2

b² = 16

b = 4 cm

we know that,

b = h = 4 cm

also ,

hypotenuse² = b² + h²
                     = 16+ 16
                     = 32

hypotenuse = √32 cm
                   = 4√2 cm

Perimeter = hypotenuse + b + h
                  = 4 √2 + 4 + 4
                  = 4√2 + 8
                  = 4(√2 + 2) cm