Question

A rectangle garden has one side that is 6 feet longer than the other. A lawn care company installs synthetic grass that costs $8 per square foot in the entire.

If x represents the length, in feet, of the shorter side of the garden, and y represents the total cost, in dollars, to install the synthetic grass, which equation correctly shows the relationship between x and y?

Answer 1

Explanation:

The area of the rectangle garden can be expressed as:

Area = Length × Width

Since one side is 6 feet longer than the other, we can express the length as:

Length = Width + 6

Substituting this expression for length into the area formula, we get:

Area = (Width + 6) × Width

Simplifying this expression, we get:

Area = Width² + 6Width

The cost to install synthetic grass is given as $8 per square foot, so the total cost y can be expressed as:

y = 8(Area)

Substituting the expression for area that we found earlier, we get:

y = 8(Width² + 6Width)

Simplifying this expression, we get:

y = 8Width² + 48Width

Therefore, the equation that correctly shows the relationship between x (the length of the shorter side of the garden) and y (the total cost to install synthetic grass) is:

y = 8x² + 48x