# 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?

Sep 8, 2015

Length= 9.5", Width = 6"

#### Explanation:

Start off with the perimeter equation: P = $2 l$ + $2 w$. Then fill in what information we know. The Perimeter is 31" and the length is equal to the width + 3.5". Therefor: 31 = $2 \left(w + 3.5\right)$ + $2 w$ 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: $12 = 2 w$. 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 : $31 = 2 l + 2 \left(6\right)$ Using the inverse of PEMDAS we subtract 12 from 31 giving 19 and we're left with $19 = 2 l$. 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 $31 = 2 \left(9.5\right) + 6 \left(2\right)$ (it is).