SOLUTION: A rectangular parking lot has a length that is 4 yards greater than the width.The area of the parking lot is 140 square yards. Find the length and the width of the parking lot?
Question 370419: A rectangular parking lot has a length that is 4 yards greater than the width.The area of the parking lot is 140 square yards. Find the length and the width of the parking lot? Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! Let w = the width. (I like choosing the smaller number for the variable. That way I get to use addition or multiplication to express the larger value. For most people adding and multiplying are easier to work with.)
Then if the length is 4 yards greater, then the length would be w+4.
For a rectangle, A = l*w. Replacing A with the given area, 140, and l with w+4 we get:
(140) = (w+4)*w
Note how I used parentheses when replacing A and l. It is an extremely good habit to do this. On the left side the parentheses don't make much difference. But on the right side it helps us see that the Distributive Property will be needed to multiply:
This is a quadratic equation (because of the squared term). To solve it we want one side of the equation to be zero. So we will subtract 140 from each side:
Next we will factor the non-zero side (or use the Quadratic Formula. This factors pretty easily:
0 = (w+14)(w-10)
From the Zero Product Property we know that this (or any) product can be zero only if one (or more) of the factors is zero. So:
w+14 = 0 or w-10 = 0
Solving these we get:
w = -14 or w = 10
Since the width of a parking lot cannot be negative, we will reject the negative solution. This leaves w = 10. So the width of the parking lot is 10 yards and the length, which is w+4, is 10+4 or 14 yards.
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