Question

The area of an equilateral triangle is numerically equal to its perimeter. The side of triangle is ______.

Options

• `sqrt(3)` unit

• `2sqrt(3)` unit

• `3sqrt(3)` unit

• `4sqrt(3)` unit

Answer 1

The area of an equilateral triangle is numerically equal to its perimeter. The side of triangle is `underlinebb(4sqrt(3)  unit)`.

Explanation:

 Let the side be a.

Perimeter = 3a and area = `sqrt(3)/4 a^2`.

Set `sqrt(3)/4 a^2 = 3a`; for a > 0 divide by a to get `sqrt(3)/4 a = 3`, so `a = 12/sqrt(3) = 4sqrt(3)`.

This uses the equilateral-triangle area formula `sqrt(3)/4 a^2`.