Question

The picture shows an equilateral triangle cut into 2 halves by a line through a vertex A.

What is the difference between the perimeter of the triangle ABC and the perimeter of ABO?

• A. 3 + $\sqrt{3}$ units
• B. $\sqrt{3}$ units
• C. 3 - $\sqrt{3}$ units
• D. 3 units

Answer 1

The correct option is C

3 - $\sqrt{3}$ units

In the given figure AB = 2 and AC = 2 units

OB = PC = 1 unit

$\therefore$ OA = $\sqrt{2^2-1^2}$ = $\sqrt{3}$ units

The perimeter of triangle ABO
= 2 + 1 + $\sqrt{3}$ = 3 + $\sqrt{3}$ units

The Perimeter of the Equilateral triangle ABC was = 2 + 2 + 2 = 6 units

$\therefore$ Difference in Perimeter
= 6 - (3 + $\sqrt{3}$) = 3 - $\sqrt{3}$ units