Question

Sum of all perpendiculars drawn is a cm. Find the perimeter of an equilateral triangle.

1. √3a cm
2. 4√3a cm
3. 2/√3a cm
4. 2√3a cm

Answer 1

Correct Answer - Option 4 : 2√3a cm

Calculations:

All sides of an equilateral triangle are equal.

Sum of three perpendiculars of an equilateral triangle = height of triangle

Height of triangle = a cm

Side of an equilateral triangle = 2/√3 × a

∴ Perimeter of an equilateral triangle = 3 × 2a/√3 = 2√3a cm.

For equilateral triangle: The sum of all the three lengths = height of equilateral triangle