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