Question

the length of a rectangular sign is 3 times its width. if the signs perimeter is 32 inches, what is the signs area?
solve on paper. then check your answer on zearn.
the signs area is
square inches.

Explanation:

Step1: Set up variables

Let the width of the rectangular sign be \( w \) inches. Then the length \( l = 3w \) inches.

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \( P=2(l + w) \). Substitute \( l = 3w \) into \( P = 32 \):
\( 32=2(3w+w) \). Simplify the right - hand side: \( 32 = 2\times4w=8w \). Solve for \( w \): \( w=\frac{32}{8}=4 \) inches.

Step3: Find the length

Since \( l = 3w \), then \( l=3\times4 = 12 \) inches.

Step4: Calculate the area

The area formula for a rectangle is \( A=l\times w \). Substitute \( l = 12 \) and \( w = 4 \): \( A=12\times4=48 \) square inches.

Answer:

48