Math CentralQuandaries & Queries


Question from Ash:

I need to know how to figure out the dimensions of a rectangle. I know that the
area is 30ft and the perimeter is 26ft. I'm 15 and I have no idea what I'm
supposed to do.


Hi Ash,

I would first draw a diagram


The dimensions of a rectangle are its length and its width. I used $L$ to designate the length and $W$ to designate its width.

The area of a rectangle is its length times its width so

\[L \times W = 30 \mbox{ square feet}\]

and its perimeter is the distance all the way around so

\[L + W + L + W = 26 \mbox{ feet.}\]

Hence the distance half way around is

\[L + W = 13 \mbox{ feet.}\]

Thus you have two equations

\[L \times W = 30 \]


\[L + W + 13.\]

Do you know two numbers with a sum of 13 and a product of 30?


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