Question

the length and width of a rectangle are consecutive integers. the perimeter of the rectangle is 26 inches. find the length and width of the rectangle. answer attempt 1 out of 2 width = \boxed{1} inches length = \boxed{} inches submit answer

Explanation:

Step1: Define variables

Let the width be \( x \) inches. Since length and width are consecutive integers, length will be \( x + 1 \) inches.

Step2: Use perimeter formula

Perimeter of a rectangle is given by \( P = 2(\text{length} + \text{width}) \). We know \( P = 26 \), so:

$$ 2(x + (x + 1)) = 26 $$

Step3: Simplify the equation

First, divide both sides by 2:

$$ x + (x + 1) = 13 $$

Then, combine like terms:

$$ 2x + 1 = 13 $$

Subtract 1 from both sides:

$$ 2x = 12 $$

Divide both sides by 2:

$$ x = 6 $$

Step4: Find length

Length is \( x + 1 = 6 + 1 = 7 \) inches.

Answer:

Width = 6 inches, Length = 7 inches