Question

The length of a rectangle is five times its width. If the area of the rectangle is 320m, find the perimeter

Answer 1

Answer: The perimeter is 96 m

Step-by-step explanation:

If we tag the length of the rectangle as $l$ and the width as $w$, and if in addition we are told $l=5 w$,the dimensions of the rectangle are as shown in the figure.

Now, the area of a rectangle is given by:

$A=(l)(w)=320 m^{2}$

Since $l=5 w$:

$A=(5w)(w)=320 m^{2}$

Isolating $w$:

$5w^{2}=320 m^{2}$

$w=\sqrt{\frac{320 m^{2}}{5}}$

$w=8 m$

On the other hand, the perimeter of a triangle is given by the addition of each of its sides. Then, if the rectangle has two sides that measure $w$ and two sides that measure $5 w$, the perimeter is:

$P=2(5)(w)+2w$

Substituting the value of $w$ in the last equation:

$P=2(5)(8 m)+2(8 m)$

Finally the perimeter is:

$P=96 m$