Question

Each of the equal sides of an isosceles triangle is 2 cm more than its height. If the base of triangle is 12 cm, then the area of triangle is ______.

Options

• 24 cm²

• 36 cm²

• 48 cm²

• 72 cm²

Answer 1

Each of the equal sides of an isosceles triangle is 2 cm more than its height. If the base of triangle is 12 cm, then the area of triangle is 48 cm².

Explanation:

Let the height = h and each equal side = h + 2.

The height and half the base `12/2 = 6` form a right triangle with the equal side as hypotenuse: 

(h + 2)² = h² + 6²

⇒ h² + 4h + 4 = h² + 36

⇒ 4h = 32

⇒ h = 8 cm 

Area = `1/2` × base × height 

= `1/2 xx 12 xx 8`

= 48 cm²