Question

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

Answer 1

Let abc be the isosceles right triangle.

 

ac = hypotenuse;

 

ab = height;

 

bc = base

 

Area of the triangle = ½*base*height

 

 Let height = base = x cm, since abc is a isosceles triangle.

 

Hence, 8 = ½*x*x

 

           16 = [x]2

 

Therefore, x =  √16

 

                    x = 4cm

 

In right angled triangle abc,

 

By using Pythagoras theorem,

 

[ab]2+ [bc]2= [ac]2

 

[4]2+ [4]2= [ac]2

 

16 + 16 = [ac]2

 

Hence, [ac]2= 32

 

              ac = √32

 

              ac = 4√2 = length of hypotenuse

 

Therefore the length of the hypotenuse is 4√2 cm= 5.656 cm