Question

The length of a rectangle is 3.5 inches more than its width. The perimeter of the rectangle is 31 inches. How do you find the length and width of the rectangle?

Answer 1

Length= 9.5", Width = 6"

Explanation:

Start off with the perimeter equation: P = `2l` + `2w`. Then fill in what information we know. The Perimeter is 31" and the length is equal to the width + 3.5". Therefor: 31 = `2(w + 3.5)` + `2w` because `l = w + 3.5`.

Then we solve for `w` by dividing everything by 2. We are then left with `15.5 = w + 3.5 + w`. Then subtract `3.5` and combine the `w`'s in order to get: `12 = 2w`. Finally divide by 2 again to find `w` and we get `6 = w`. This tells us the width is equal to 6 inches, half the problem.

In order to find the length we simply plug the new found information of width into our original perimeter equation. So : `31 = 2l + 2(6)` Using the inverse of PEMDAS we subtract 12 from 31 giving 19 and we're left with `19 = 2l`. So now we just divide by two in order to get the length which is `9.5` inches

Finally we need to check our equation to make sure everything works so ask yourself is `31 = 2(9.5) + 6(2)` (it is).