Question

The base of an isosceles triangle is 40 cm and its area is 420 cm². Find the length of its equal sides.

Answer 1

Given:

• Base (B) of an isosceles triangle = 40 cm
• Area (A) = 420 cm²
• Length of equal sides = ?

Stepwise calculation:

Let the length of each equal side = a cm.

In an isosceles triangle, the altitude (height, h) bisects the base, so the height divides the base into two equal parts of 20 cm each.

Area of triangle formula:

A = `1/2` × base × height

Substituting the values: 

`420 = 1/2 xx 40 xx h`

⇒ `h = (420 xx 2)/40`

⇒ h = 21 cm

Using the Pythagoras theorem on the right triangle formed by the height, half of the base and the equal side:

`a^2 = h^2 + (b/2)^2`

= 21² + 20²

= 441 + 400

= 841

a = `sqrt(841)`

a = 29 cm

The length of each of the equal sides is 29 cm.