Answer to Question #315386 in Geometry for savannah

Question

The length of the base of a rectangular prism is twice its width. The perimeter of the base is 42 yards. If the volume of the prism is 980 cubic yards, find the height of the prism.

Answer 1

The volume of a rectangular prism is the product of its three dimensions V=l*w*h, where l is length, w is width and h is height. It means that $h=\frac{V}{lw}$ . For the first, lets find length and width of the prism. The perimeter P=2(l+w) and in our case l=2w, so 42=2(2w+w)=6w, from what w=7 yards and l=14 yards. Finally, $h=\frac{V}{lw}=\frac{980}{14*7}=\frac{980}{98}=10$ yards.

Answer: h=10 yards.