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?

Question

A.

Answer 1

To find the equation that can be used to determine the possible values for the length of Gabby's backyard, let's define the variables:

• Let $x$ be the length of the backyard (in meters).
• Since the width is 4 meters shorter than the length, the width can be expressed as $x-4$ meters.

The area of a rectangle can be calculated using the formula:

$$\text{Area}=\text{Length}\times \text{Width}$$

According to the information provided, the area of Gabby's backyard is 120 square meters. Therefore, we can set up the equation as follows:

$$x\cdot (x-4)=120$$

This can be simplified or rearranged to:

$$x^2-4x-120=0$$

Thus, the equation that can be used to find the possible values for the length $x$ of Gabby's backyard is:

$$x^2-4x-120=0$$