find the length of the side and perimeter of an equilateral triangle whose height is underroot 3cm by pythagoras theorem
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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 = x²
x²+12 = 4x²
12 = 3x²
x² = 4
x = 2
so the side length is 2, and the perimeter is 6
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 = x²
x²+12 = 4x²
12 = 3x²
x² = 4
x = 2
so the side length is 2, and the perimeter is 6
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