A rectangular patio is 9 ft by 6 ft. When the length and width are increased by the same amount,the area becomes 88 sq ft. Ginger is using the zero product property to solve the equation (6+x)(9+x)=88 What does the value of x in her solutions represent? one possible length and one possible width two possible amounts for the widths two possible amounts for the lengths two possible amounts by which the dimensions were changed

## Step 1<br />The problem involves a rectangular patio with dimensions 9ft by 6ft. The length and width of the patio are increased by the same amount, represented by \(x\), to form a new rectangle with an area of 88 sq ft. The equation \((6+x)(9+x)=88\) is derived from this situation.<br /><br />## Step 2<br />The equation \((6+x)(9+x)=88\) is a quadratic equation, which is a special type of polynomial equation. The solutions to this equation are the values of \(x\) that make the equation true.<br /><br />## Step 3<br />The solutions to the equation represent the amount by which the dimensions of the patio were changed. This is because the equation is derived from the situation where the length and width of the patio are increased by the same amount, represented by \(x\).<br /><br />## Step 4<br />The solutions to the equation do not represent the lengths or widths of the patio, nor do they represent the amounts by which the lengths or widths were changed. They represent the amount by which both the length and the width were changed.