A rectangular solid has a base area of 43.3 sq inches and a height of 50 inches a triangular prism has a base in the shape of an equilateral triangle and a height of 50 inches. the volumes for both shapes are equal. find the side of the equilateral triangle for the base of the prism to the nearest inch.
43.3
To find the side of the equilateral triangle for the base of the prism, we can start by calculating the volume of each shape.
The volume of a rectangular solid is given by the formula:
Volume = Base Area * Height
Since you already have the base area (43.3 sq inches) and the height (50 inches), you can calculate the volume of the rectangular solid.
Volume of Rectangular Solid = 43.3 sq inches * 50 inches
Volume of Rectangular Solid = 2150 cubic inches
The volume of a triangular prism is given by the formula:
Volume = (Base Area * Height) / 2
Since the height of the triangular prism is also 50 inches, we can set up an equation to find the side length of the equilateral triangle.
(43.3 sq inches * 50 inches) / 2 = (Side Length of Equilateral Triangle * Side Length of Equilateral Triangle * √3) * 50 inches / 2
Simplifying this equation:
(43.3 * 50) / 2 = (Side Length of Equilateral Triangle * Side Length of Equilateral Triangle * √3) * 50 / 2
2150 = (Side Length of Equilateral Triangle * Side Length of Equilateral Triangle * √3)
To find the side length of the equilateral triangle, we can divide both sides of the equation by √3:
2150 / √3 = Side Length of Equilateral Triangle * Side Length of Equilateral Triangle
To find the square root of both sides, we get:
√(2150 / √3) = Side Length of Equilateral Triangle
Calculating this value:
Side Length of Equilateral Triangle ≈ 35.29 inches (rounded to the nearest inch)
Therefore, the side length of the equilateral triangle for the base of the prism is approximately 35 inches.