The perimeter of a rectangle is 64 feet. Find its dimensions assuming that its length is 7 feet less than twice its width.

To find the dimensions of the rectangle, we can start with the formulas for perimeter and the relationship between length and width. The perimeter \( P \) of a rectangle is given by the formula \( P = 2L + 2W \). Given that the perimeter is 64 feet, we can write the equation as \( 2L + 2W = 64 \) or simplified to \( L + W = 32 \). Next, we know that the length \( L \) is 7 feet less than twice the width \( W \). This can be expressed as \( L = 2W - 7 \). Now we can substitute this expression for \( L \) into the perimeter equation: \[ (2W - 7) + W = 32 \] Combining like terms gives us: \[ 3W - 7 = 32 \] Adding 7 to both sides results in: \[ 3W = 39 \] Dividing by 3 gives us the width: \[ W = 13 \text{ feet} \] Now substitute \( W \) back into the expression for \( L \): \[ L = 2(13) - 7 = 26 - 7 = 19 \text{ feet} \] Thus, the dimensions of the rectangle are a length of 19 feet and a width of 13 feet. In a real-world application, understanding rectangles is crucial in fields ranging from architecture to flooring. When designing spaces or laying out materials, knowing the perimeter helps professionals estimate costs and ensure proper fit. Many people trip up when dealing with formula substitutions, especially when running into relationships like "7 feet less than". Visualizing or sketching out the problem can often clarify these relationships and prevent errors in calculations that lead to incorrect dimensions!