To find: the find the distance x by which the parking lot must be expanded so that it doubles in the area.
Given information:
The grocery store wants to double the area of its parking lot by expanding the old parking lot as shown:
Formula Used:
Property Used:
Zero Product property: If product of two expressions is zero, then either one or both the expressions equal zero.
Calculation:
From the given picture, it is clear that the grocery is rectangular-shaped. And its length of is 300 ft, while its width is 165 ft.
So,
The area of the grocery store and the old parking lot combined is:
So, the area of the old parking lot is:
The grocery store wants to double the area of the parking lot. So, the area of the new parking lot is:
Thus, the area of the grocery store combined with the area of the new parking lot is:
Now, by looking the given diagram, it can be seen that the after expanding by x , the new area that is the combined area of the grocery store and the new parking lot is:
So, the new area is:
But, as obtained above, the area of the grocery store combined with the area of the new parking lot is
Multiply using FOIL,
Combine the like terms,
Subtract 130500 from both sides,
Factor the above equation,
Then, by zero product property,
Solve for x ,
Since the grocery store wants to double the area of the parking lot, so the value of x can’t be negative. So, the only solution to the given problem is:
Thus, the length and the width must be increased by 60 feet.
Chapter 1 Solutions
EBK ALGEBRA 2
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