Question

What is the length to the nearest tenth of the altitude of an equilateral triangle with a perimeter of 30 inches

Answer 1

The altitude of an equilateral triangle with a perimeter of 30 inches is 0 inches.

Step-by-step explanation:

An equilateral triangle has all three sides of equal length. Since the perimeter of the triangle is 30 inches, each side will be 30/3 = 10 inches.

The altitude of an equilateral triangle divides the triangle into two congruent right triangles. To find the length of the altitude, we can use the Pythagorean theorem.

Let's call the length of the altitude h. Using the Pythagorean theorem, h^2 = (10/2)^2 - 5^2 = 25 - 25 = 0. Taking the square root of both sides, we find that h = 0. The altitude of the equilateral triangle is 0 inches.

Answer 2

Each side of an equilateral triangle = perimeter / 3.
Each side = 10 inches.
The altitude divides the triangle into two 30 60 90 triangles. The hypotenuse is 10 inches and the short side is 5 inches.
altitude^2 = 10^2 - 5^2
altitude^2 = 100 - 25
altitude^2 = 75
altitude = 8.6602540378