Answer:
Step-by-step 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:
[tex]x^{2} = (\frac{x}{2})^{2} + (2\sqrt{3})^{2}\\ x^{2} = \frac{x^{2}}{4} + 12\\ 4x^{2} = x^{2} + 48\\ 3x^{2} = 48\\ x^{2} = 16\\x = \frac{+}{}4\\ \\[/tex]
x must be positive as it is a length so we multiply 4 by 3 to get the perimeter of 12.
