A rectangular field is 4 times as long as it is wide. If the perimeter of the field is 500 yards what are the fields dimensions?

Mar 21, 2018

$\text{length "=200" yards and width "=50" yards}$

Explanation:

$\text{let the width } = w$

$\text{then length "=4wlarrcolor(blue)"4 times the width}$

• " perimeter "=(2xx"length")+(2xx"width")

$\textcolor{w h i t e}{\times \times \times \times \times} = 8 w + 2 w = 10 w$

$\text{now perimeter "=500" yards}$

$\Rightarrow 10 w = 500$

$\text{divide both sides by 10}$

$\frac{\cancel{10} w}{\cancel{10}} = \frac{500}{10}$

$\Rightarrow w = 50 \text{ yards "larrcolor(blue)"width}$

$\Rightarrow 4 w = 4 \times 50 = 200 \text{ yards"larrcolor(blue)"length}$

$\textcolor{b l u e}{\text{As a check}}$

$\left(2 \times 50\right) + \left(2 \times 200\right) = 100 + 400 = 500 \leftarrow \text{Correct}$