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.