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Answer

= 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


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