Question

the length of a rectangle is 6 in longer than its width.
if the perimeter of the rectangle is 52 in, find its area.
$square$ in$^2$

Explanation:

Step1: Define variables for width

Let width = $w$

Step2: Define length in terms of width

Length = $w + 6$

Step3: Set up perimeter equation

Perimeter formula: $2(\text{length} + \text{width}) = 52$
Substitute values: $2(w + 6 + w) = 52$

Step4: Simplify and solve for $w$

Simplify inside parentheses: $2(2w + 6) = 52$
Divide both sides by 2: $2w + 6 = 26$
Subtract 6 from both sides: $2w = 20$
Solve for $w$: $w = \frac{20}{2} = 10$

Step5: Calculate length

Length = $10 + 6 = 16$

Step6: Calculate area

Area formula: $\text{length} \times \text{width}$
Substitute values: $16 \times 10$

Answer:

160 $\text{in}^2$