Question

Find the area and perimeter of an isosceles right triangle, each of whose equal sides measures 10 cm. [Take `sqrt(2) = 1.41`.]

Answer 1

Let:

Length of each of the equal sides of the isosceles right-angled triangle = a = 10 cm

And. 

Area of isosceles right – angled triangle=`1/2xxBasexxHeight` 

The hypotenuse of an isosceles right – angled triangle can be obtained using Pythagoras’ theorem 

If h denotes the hypotenuse, we have: 

`h^2=a^2+a^2` 

⇒`h=2a^2` 

⇒`h=sqrt2a` 

⇒`h=10sqrt2 cm`` 

∴ Perimeter of the isosceles right-angled triangle = `2a+sqrt2a` 

=`2xx10+1.41xx10` 

=`20+14.1` 

=`34.1 cm`