A diagonal of the front face of a rectangular prism is 13 inches long, and a diagonal of the top face of the same prism is 15 inches long. The height of the front face of the prism is 5 inches long. How many cubic inches are in the volume of the prism if each of the dimensions is an integer length?
+129840 A diagonal of the front face of a rectangular prism is 13 inches long, and a diagonal of the top face of the same prism is 15 inches long. The height of the front face of the prism is 5 inches long. How many cubic inches are in the volume of the prism if each of the dimensions is an integer length?
Using the Pythagorean Theorem, the widrh of the front face = √[13^2 - 5^2] =
√[169 - 25 ] = √144 = 12 in = one base dimension
The other side of the top = the other base dimension = √[ 15^2 - 12^2] = √[225 - 144] = √ 81 = 9in
So...the volume of the prism = Area of a base * height = (12 * 9) * 5 =
108 * 5 = 540 in^3
