Question

the length of a rectangle is 5 in longer than its width.
if the perimeter of the rectangle is 58 in, find its length and width.
length: □ in
width: □ in

Explanation:

Step1: Define variables for width

Let width $= w$ inches.

Step2: Define length in terms of w

Length $= w + 5$ inches.

Step3: Use perimeter formula

Perimeter of rectangle: $2(\text{length} + \text{width}) = 58$
Substitute values: $2((w+5) + w) = 58$

Step4: Simplify and solve for w

$2(2w + 5) = 58$
$4w + 10 = 58$
$4w = 58 - 10$
$4w = 48$
$w = \frac{48}{4} = 12$

Step5: Calculate length

Length $= 12 + 5 = 17$

Answer:

length: 17 in
width: 12 in