Question

The base of an isosceles triangle is 6 cm and its area is 12 sq. cm. Find its perimeter.

Answer 1

Given: Base = 6 cm, Area = 12 cm² (isosceles triangle)

Step-wise calculation:

1. Area formula:

Area = `1/2` × base × height

2. Solve for height:

height = `(2 xx "Area")/"base"`

= `(2 xx 12)/6`

= 4 cm

3. Half the base

= `6/2` 

= 3 cm

In the right triangle formed, equal side

= `sqrt("half‑base"^2 + "height"^2)` 

= `sqrt(3^2 + 4^2)` 

= `sqrt(9 + 16)`

= `sqrt(25)`

= 5 cm

4. Perimeter = base + 2 × (equal side)

= 6 + 2 × 5 

= 16 cm

The perimeter of the triangle is 16 cm.