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

rk193140 rk193140    1   14.02.2022 02:50    7

Answers
brookebeatrice8 brookebeatrice8  14.02.2022 02:50

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:

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\\ \\

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

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