jmc

Question

If a rectangular prism has a length of l, a width of w, and a height of h, then the length of its diagonal is equal to l^2 + w^2 + h^2. Suppose l = 3 and h = 12; if the length of the diagonal is 13, what is the width?

Accepted Answer

We are given that l^2 + w^2 + h^2 = 3^2 + w^2 + 12^2 = 153 + w^2 = 13.Squaring both sides, it follows that 153 + w^2 = 13^2 = 169 w = 4.Since the width must be a positive quantity, the answer is 4.