Question

the length of a rectangular sign is 5 times its width. if the signs perimeter is 36 inches, what is the signs area? solve on paper. then check your answer on zearn. the signs area is square inches.

Explanation:

Step1: Let the width be $w$.

The length $l = 5w$.

Step2: Use the perimeter formula.

The perimeter of a rectangle $P=2(l + w)$. Given $P = 36$, so $2(5w+w)=36$.

Step3: Simplify the equation.

$2\times6w=36$, which is $12w = 36$.

Step4: Solve for $w$.

$w=\frac{36}{12}=3$ inches.

Step5: Find the length.

Since $l = 5w$, then $l=5\times3 = 15$ inches.

Step6: Calculate the area.

The area of a rectangle $A=l\times w$, so $A=15\times3=45$ square - inches.

Answer:

45