Question

The area of the isosceles triangle is `5/4 sqrt(11)` cm², if the perimeter is 11 cm and the base is 5 cm.

पर्याय

• True

• False

Answer 1

This statement is True.

Explanation:

Suppose that side of isosceles triangle be a.

Now, perimeter of an isosceles triangle:

2s = 5 + a + a  ...[2s = a + b + c]

11 = 5 + 2a

2a = 11 – 5

2a = 6

a = 3

Now, the formula of an area of isosceles triangle = `a/4 sqrt(4b^2 - a^2)`

So, area of an isosceles triangle = `(5sqrt(4 xx (3)^2 - (5)^2))/4`

= `(5sqrt(4 xx 9 - 25))/4`

= `5 xx sqrt(36 - 25)/4`

= `(5sqrt(11))/4` cm²