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: Let the width be \( w \)

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

Step2: Use the perimeter formula

The perimeter formula of a rectangle is \( P=2(l + w) \). Substitute \( l = 3w \) and \( P = 32 \) into the formula:

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Solve for \( w \): \( w=\frac{32}{8}=4 \) inches.

Step3: Find the length

Since \( l = 3w \), when \( w = 4 \), \( l=3\times4 = 12 \) inches.

Step4: Calculate the area

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

Answer:

48