Answer
270 square feet
Work Step by Step
Since the width is stated in terms of the length, we can let l represent the length.
The width is 1 more than one-third of the length, which is l, so the width is 1 + $\frac{1}{3}$l.
The formula for the perimeter of the rectangle is width + width + length + length
The perimeter of the rectangle is 74, so we set up the following equation:
l + l + 1 + $\frac{1}{3}$l + 1 + $\frac{1}{3}$l = 74
2l + 2 + $\frac{2}{3}$l = 74
$\frac{6l}{3}$ + 2 + $\frac{2}{3}$l = 74
Subtract 2 from both sides.
$\frac{6}{3}$l + $\frac{2}{3}$l = 72
$\frac{8}{3}$l = 72
Divide both sides by $\frac{8}{3}$
l = 72 $\div$ $\frac{8}{3}$
l = 72 $\times$ $\frac{3}{8}$
l = 27
Since the length is 27, the width is 1 + $\frac{1}{3}$ $\times$ 27 = 10.
Area= $l \times w$, so we obtain:
$A=27 \times 10 = 270 $ square feet.
