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?

1 Answer
Shail P.
Sep 8, 2015

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).

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