Question

The length of a side of an equilateral triangle is 14 centimeters.

What is the length of the altitude of the triangle?


2√ 7cm


3√ 7 cm


7√ 2 cm

7√ 3 cm

Answer 1

Answer: The altitude of the triangle is
`h = 7 √(3).`

Explanation:

Suppose that we separate the equilateral triangle with the altitude of the triangle, as shown in the diagram I attached.

Then the length of the altitude
`h` can be found through the Pythagorean theorem:

`h = \sqrt{14^2-\left( (14)/(2) \right)^2} = √(147) = \boxed{7 √(3)}.`

Therefore, the altitude of the equilateral triangle is
`h = 7 √(3).`