SOLUTION: The width of a rectangle is 3 ft less than the length. The area of the rectangle is 88 ft2. Find the length L and width W of the rectangle
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Question 1179368: The width of a rectangle is 3 ft less than the length. The area of the rectangle is 88 ft2. Find the length L and width W of the rectangle
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
if the width of a rectangle is less than the length, then we have
....eq.1
if the area of the rectangle is , we have
........substitute
...factor
=> or -> disregard negative solution for length
go to
....eq.1, substitute
the length of the rectangle and width of the rectangle
Answer by greenestamps(13209) (Show Source): You can put this solution on YOUR website!
Mentally, in five seconds or less: 88 = 11*8
Algebraically....
x = length
x-3 = width
The area (length times width) is 88:
Factor the quadratic:
The length is either 11 or -8; since -8 makes no sense, it is 11. And then the width is 8.
Note that, in the formal algebraic solution, it was necessary to factor a quadratic equation by finding two numbers whose difference is 3 and whose product is 88; and that is what was required to solve the original problem mentally.
So the formal algebraic solution didn't make solving the problem any easier....
Nevertheless, it is a good exercise for a beginning algebra student to be able to set the problem up and solve it using formal mathematics.
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