Practice: Models and Applications

Question

The length of a rectangle is three more than double the width. If the perimeter is 90 inches, find the dimensions.

Answer 1

Let's set up a system of equations to solve this problem. If the perimeter is 90 inches, then we know that 2w+2l = 90, where w and l are the width and length of the rectangle. If we know that the length is 3 more than double the width, we can write the equation l = 2w + 3. Substituting this into the first equation, we have 2w + 2(2w + 3) = 90, and get 2w + 4w + 6 = 90, 6w = 84, and w = 14. Plugging this into the second equation to solve for the length, we get l = 2(14) + 3 = 31.