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

Dec 3, 2016

$15 \times 20$ 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:

$300 = x \left(35 - x\right)$

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:

$5 \cdot 60 \text{ }$ with $\text{ } 5 + 60 = 65$

$10 \cdot 30 \text{ }$ with $\text{ } 10 + 30 = 40$

$\textcolor{b l u e}{15 \cdot 20} \text{ }$ with $\text{ } \textcolor{b l u e}{15 + 20 = 35}$