The owner of an office building is expanding the length and width of a parking lot by the same amount.The lot currently measures 120 ft by 80 ft, and the expansion will increase its area by 4,400ft^2 By how many feet should the length of the parking lot be increased? 1.2 ft 20 ft 66.3 ft 220 ft

## Step 1<br />The problem involves the area of a rectangle, which is given by the formula:<br />### **Area = length * width**<br />The owner of the office building is expanding the parking lot by increasing both the length and the width by the same amount. Let's denote this amount as \(x\).<br /><br />## Step 2<br />The new dimensions of the parking lot will be \((120+x)\) feet by \((80+x)\) feet. The area of the expanded parking lot is given as 4,400 square feet.<br /><br />## Step 3<br />We can set up an equation to represent the area of the expanded parking lot:<br />### **(120+x) * (80+x) = 4,400**<br /><br />## Step 4<br />Expanding the left side of the equation gives us:<br />### **9,600 + 200x + x^2 = 4,400**<br /><br />## Step 5<br />Rearranging the equation to solve for \(x\) gives us:<br />### **x^2 + 200x - 5,200 = 0**<br /><br />## Step 6<br />This is a quadratic equation, which can be solved using the quadratic formula:<br />### **x = [-b ± sqrt(b^2 - 4ac)] / (2a)**<br /><br />## Step 7<br />Substituting the values of a, b, and c from our equation into the quadratic formula gives us:<br />### **x = [-200 ± sqrt((200)^2 - 4*1*(-5,200))] / (2*1)**<br /><br />## Step 8<br />Solving this equation gives us two possible values for \(x\), but since we are looking for a physical length, we only consider the positive root.