Question

The altitude of an equilateral triangle is 4.5 in. Find it's sides.

Answer 1

The length of each side is 3√3 in or 5.20 in to the nearest hundredth.-

Explanation:

The altitude splits up the triangle into two 30-60-90 triangles.

The ratio of the sides of these triangles is 2:1:√3.

The ratio of the altitude to the hypotenuse ( which is the side of the equilateral triangle ) = √3 : 2 so we have the equation:

2 / √3 = h / 4.5 where h is the required side.

h = 2*4.5 / √3

= 9 /√3

= 3 √3

= 5.196 in.

Answer 2

Explanation:

Let the length of each side be x. We can divide the triangle into two to get two right angled triangles which side will be x (hypotenuse), 4.5 (height), x/2 for base.

Using Pythagoras's theorem

x² = 4.5² + (x/2)²

x² = 81/4 + x²/4

x² - x²/4 = 81/4

3/4x² = 81/4

x² = 27

x = √27 = 3√3 in