Question 1198616: The width of a rectangle is the length minus 6 units. The area of the rectangle is 27 units. What is the length and width of the rectangle?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! A = area
L = length
W = width
A = L * W
W = L - 6
A = L * (L - 6)
A = 27
27 = L * (L - 6)
L * (L - 6) = L^2 - 6L
27 = L^2 - 6L
subtract 27 from both sides of that equation to get:
L^2 - 6L - 27 = 0
factor that quadratic equation to get:
(L - 9) * (L + 3) = 0
L = 9 or L = -3.
L can't be -3, so L = 9
W = L - 6 makes W = 3
dimensions are:
L = 9
W = 3
A = L * W = 9 * 3 = 27
length of the rectangle is 9 units and width of the rectangle is 3 units.
that's your solution.
requirements of the problem are solved, since length of 9 units minus 6 units is equal to 3 units which is the width.
Answer by MathTherapy(10556)  (Show Source):
You can put this solution on YOUR website! The width of a rectangle is the length minus 6 units. The area of the rectangle is 27 units. What is the length and width of the rectangle?
All you need for this is 2 numbers that have a product of 27, and a difference of 6. Obviously those 2 numbers are 9 amnd 3.
Since the length is the longer of the 2, and the width is the shorter, LENGTH = 9, and WIDTH = 3.
You DON'T NEED equations to solve this. As a matter oof fact, if you do use equations, you come right back to asking yourself
the same question in order to solve the equation: "What 2 numbers have a product of 27, and a difference of 6."
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