Question

What is the perimeter of an equilateral triangle whose height is 2 square root of 3

Answer 1

Explanation:

If we half the base of the equilateral triangle, which has a length of xcm, we can form a right-angled triangle with a base of x/2 cm and height 2√3 cm.

Now using Pythagoras' Theorem we solve for the hypotenuse:

`x^(2) = ((x)/(2))^(2) + (2√(3))^(2)\\ x^(2) = (x^(2))/(4) + 12\\ 4x^(2) = x^(2) + 48\\ 3x^(2) = 48\\ x^(2) = 16\\x = \frac{+}{}4\\ \\`

x must be positive as it is a length so we multiply 4 by 3 to get the perimeter of 12.

Answer 2

the answer for this is 12