The width of Gabby's backyard is 4 meters shorter than its length, and its area is equal to 120 square meters. Which equation can be used to find the possible values for the length of Gabby's backyard, x?

Answer 1

Let the length of Gabby's backyard be denoted as \( x \) meters. According to the problem, the width is 4 meters shorter than the length, so we can express the width as \( x - 4 \) meters.

The area of a rectangle is given by the formula:

\[ \text{Area} = \text{Length} \times \text{Width} \]

Substituting the expressions we have for the length and width into this formula, we can set up the equation for the area:

\[ x(x - 4) = 120 \]

Now, this equation can be rearranged into a standard quadratic form:

\[ x^2 - 4x - 120 = 0 \]

This is the equation that can be used to find the possible values for the length \( x \) of Gabby’s backyard.