Answer
Length = 16ft
Width = 11ft
Work Step by Step
Recall the formula for the area of a rectangle:
$$A=LW$$
Given: L = 5 + W; A=176
Substitute these to the formula:
$$A=LW$$ $$176=(5 + W)W$$ $$176=5W + W^2$$
Subtract $176$ from both sides:
$$176-176=5W + W^2-176$$ $$5W + W^2-176=0$$
Factor:
$$(W+16)(W-11)=0$$
$$W+16=0 \: or \: W-11=0$$
$$W=-16$$ $$W=11$$
Since measurements cannot be negative, therefore the width is equal to $11ft$.
Substitute this value to the formula of area:
$$A=LW$$
$$176=L(11)$$
Divide both sides by $11$.
$$\frac{176}{11}=\frac{L(11)}{11}$$
$$L=16$$
Thus, the length is equal to $16ft$.
