Question

the perimeter of a rectangle is 260 feet. find the length and width if the length is an even integer and the width is 5 times the next consecutive even integer.
answer attempt 1 out of 5
length = \boxed{} feet width = \boxed{} feet submit answer

Explanation:

Step1: Define variables

Let the length be \( x \) (an even integer). Then the next consecutive even integer is \( x + 2 \), and the width is \( 5(x + 2) \).

Step2: Use perimeter formula

The perimeter of a rectangle is \( P = 2(\text{length} + \text{width}) \). We know \( P = 260 \), so:

$$ 2(x + 5(x + 2)) = 260 $$

Step3: Simplify the equation

First, divide both sides by 2:

$$ x + 5(x + 2) = 130 $$

Expand the brackets:

$$ x + 5x + 10 = 130 $$

Combine like terms:

$$ 6x + 10 = 130 $$

Step4: Solve for \( x \)

Subtract 10 from both sides:

$$ 6x = 120 $$

Divide both sides by 6:

$$ x = 20 $$

Step5: Find the width

The width is \( 5(x + 2) \). Substitute \( x = 20 \):

$$ 5(20 + 2) = 5 \times 22 = 110 $$

Answer:

Length = \( 20 \) feet
Width = \( 110 \) feet