Question

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

Answer 1

`15 xx 20` feet

Explanation:

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)`