Question

What is the exact height of the equilateral triangle shown below in which each side is 14 units long?

Answer 1

Answer: 12.12 units

Let us create the figure to make it easier to understand how to solve this question.

Each side measures 14 units. Since the triangle is an equilateral triangle, the height of the triangle is directly at the middle of the triangle, hence dividing it into two equal parts. This is why the base of the triangle is divided into 7s.

As we can see, the height of the triangle will create a right triangle on both sides of the triangle. Since we now have a right triangle, we can solve for the height of the triangle using the Pythagorean theorem.

The Pythagorean theorem is noted as:

`c^2=a^2+b^2`

Where:

a and b are the shorter sides of the triangle while c is the longest side of the triangle.

We have:

a = 7

c = 14

We look for b:

`\begin{gathered} c^2=a^2+b^2 \\ c^2-a^2=b^2 \\ b=\sqrt[]{c^2-a^2} \\ b=\sqrt[]{(14)^2-(7)^2} \\ b=\sqrt[]{147}=12.1243\approx12.12 \end{gathered}`

Therefore, the height of the triangle is 12.12 units.