Question

The height of an equilateral triangle is 4√3. What is the perimeter of the equilateral triangle?

a) 12 units
b) 12√3 units
c) 24 units
d) 24√3 units

Answer 1

= 24 units

Solution and explanation;

• The height of an equilateral is a perpendicular bisector of the base. It divides the triangle in two two halves forming two small right-angled triangles.

• The base of the right-angled triangle will be s/2 and the hypotenuse is s; where s is the side of the equilateral triangle;

Therefore; using the Pythagoras theorem;

S² = (S/2)² + h²; where h is the height of the equilateral triangle

S² =S²/4 + (4√3)²

S² = S²/4 + 48 ; Multiplying everywhere by 4; we get

4 S² = S² + (48×4)

3 S² = 192

S² = 64

S = 8

but, perimeter of an equilateral triangle is side × 3

Perimeter= 8 × 3

= 24 units