Question

the length of a rectangular sign is 3 times its width. if the signs perimeter is 16 inches, what is the signs area? solve on paper. then check your answer on zearn. the signs area is square inches.

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$. Then the length $l = 3w$.

Step2: Use perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Substitute $l = 3w$ and $P = 16$ into it: $16=2(3w+w)$.

Step3: Simplify the equation

First, simplify the right - hand side: $16 = 2(4w)=8w$.

Step4: Solve for $w$

Divide both sides of the equation $16 = 8w$ by 8, we get $w = 2$ inches.

Step5: Find the length

Since $l = 3w$, then $l=3\times2 = 6$ inches.

Step6: Calculate the area

The area formula of a rectangle is $A=l\times w$. Substitute $l = 6$ and $w = 2$ into it: $A=6\times2=12$ square inches.

Answer:

12