Question

find the length if the side and perimetre of an equilateral triangle whose height is root 3

Answer 1

Split the triangle down the middle and you get two right triangles with a height of sqrt(3) cm. The triangle is equilateral so you know that the base is 1/2 as long as the hypotenuse. Let the hypotenuse be x. Using the pythagorean theorem:

(x/2)^2 + 3 = x^2

x^2+12 = 4x^2

12 = 3x^2

x^2 = 4

x = 2

so the side length is 2, and the perimeter is 6

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