Question

A rectangle has a length of 4 inches and a perimeter of 32 inches. Write and solve an equation to find the width of the rectangle.

Answer 1

The width of the rectangle is 10 inches.

Step-by-step explanation:

To find the width of the rectangle, we can use the formula for the perimeter of a rectangle, which is
`\( P = 2L + 2W \)`, where
`\( P \)` is the perimeter,
`\( L \)`is the length, and
`\( W \)` is the width. In this case, the length
`\( L \)` is given as 4 inches, and the perimeter
`\( P \)`is given as 32 inches.

The formula becomes
`\( 32 = 2(4) + 2W \)`. Simplifying further,
`\( 32 = 8 + 2W \)`, and by subtracting 8 from both sides, we get
`\( 24 = 2W \)`. To find the width, we divide both sides by 2, yielding
`\( W = 12 \)`.

Therefore, the width of the rectangle is 12 inches. It's crucial to understand that the width represents the distance across the shorter sides of the rectangle. This solution is consistent with the given information about the length and perimeter, ensuring the equation is correctly set up and solved to find the width of the rectangle.