Question

finding the perimeter or area of a rectangle given one of these values
try again
your answer is incorrect.
the length of a rectangle is 2 in longer than its width.
if the perimeter of the rectangle is 32 in, find its area.

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) inches. Then the length \( l \) is \( w + 2 \) inches (since length is 2 in longer than width).

Step2: Use perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know \( P = 32 \), so substitute \( l = w + 2 \) into the perimeter formula:

$$ 32 = 2((w + 2) + w) $$

Step3: Solve for width

Simplify the equation:

$$ 32 = 2(2w + 2) $$

Divide both sides by 2:

$$ 16 = 2w + 2 $$

Subtract 2 from both sides:

$$ 14 = 2w $$

Divide by 2:

$$ w = 7 $$

Step4: Find length

Since \( l = w + 2 \), substitute \( w = 7 \):

$$ l = 7 + 2 = 9 $$

Step5: Calculate area

The area \( A \) of a rectangle is \( A = l \times w \). Substitute \( l = 9 \) and \( w = 7 \):

$$ A = 9 \times 7 = 63 $$

Answer:

\( 63 \) square inches