A rectangle with perimeter $70$ feet has area $300$ square feet. What are its dimensions?

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Answer 1 · 2016-12-03T00:07:13

$15 xx 20$ feet

Let the length of one side be $x$ .

Going round the rectangle, the other sides are of lengths:

$35 - x$

$x$

$35 - x$

The area of the rectangle is:

$300 = x(35-x)$

So essentially we are looking for a pair of factors of $300$ which sum to $35$ .

Since $300$ and $35$ are both divisible by $5$ , the pair we are looking for must both be divisible by $5$ too.

So the pairs of factors we need to consider are:

$5 * 60" "$ with $" "5+60 = 65$

$10 * 30" "$ with $" "10+30 = 40$

$color(blue)(15 * 20)" "$ with $" "color(blue)(15+20 = 35)$

A rectangle with perimeter 7070 feet has area 300300 square feet. What are its dimensions?