Question

An airfreight company uses a box in the shape of a triangular prism to pack blueprints. posters, and other items that can be rolled up to fit inside the box. Each base is an equilateral triangle. The dimensions of the box are shown below. 2. What is the height of the equilateral triangles on either end of the box? Dhow or explain how you got your answer.

Answer 1

The height of the equilateral triangles on either end of the box is 5.2 inches

Step-by-step explanation:

The volume of a triangular prism = 1/2 ×base × height × length

base = 6 inches

Height = ?

length = 38 inches

We are told the triangle is an equilateral triangle. This means the three sides of the triangle are equal.

The slant sides are equal to 6 inches

The triangle was splitted into two equal parts in order to find the height.

We apply pythagoras' theorem to get the height:

Hypotenuse² = opposite² + adjacent²

Hypotenuse = 6, opposite = h, adjacent = 3

6² = h²+ 3²

36 = h²+ 9

36-9 = h²

27 = h²

h = √27 = √(3×9)

h = 3√3 = 5.2 inches

The height of the equilateral triangles on either end of the box is 5.2 inches