The diagram below represents the measurements of Jennie’s yard. The yard’s width is x feet shorter than its length. If the area of the yard is 540 square feet, how many feet shorter than the length is the width?

Question

A yard with a length of 30 feet and a width of (30 minus x) feet.

Solve the equation to find how many feet shorter than the length the width is.

30(30 – x) = 540

What is the value for x?

Answer 1

To solve the equation \( 30(30 - x) = 540 \), we can start by simplifying the left side of the equation:

1. Distribute the 30 on the left side: \[ 30 \cdot 30 - 30 \cdot x = 540 \] This simplifies to: \[ 900 - 30x = 540 \]

2. Next, isolate the term with \( x \) by subtracting 900 from both sides: \[ -30x = 540 - 900 \] \[ -30x = -360 \]

3. Now, divide both sides by -30 to solve for \( x \): \[ x = \frac{-360}{-30} = 12 \]

Thus, the value for \( x \) is \( 12 \). This means the width is 12 feet shorter than the length.