SOLUTION: Mr.Ulep has a rectangular field with a length twice its width.If 4 feet are taken from the length and 3 feet are taken from the width, the area of the field is 180 square feet.Find

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Question 1188666: Mr.Ulep has a rectangular field with a length twice its width.If 4 feet are taken from the length and 3 feet are taken from the width, the area of the field is 180 square feet.Find the area of the original field
Found 2 solutions by Shin123, ikleyn:
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
Since the length is twice the width, let's say the length is 2x and the width is x. So we have the equation %282x-4%29%28x-3%29=180. Expanding, we get 2x%5E2-10x-168=0.
Solved by pluggable solver: Completing the Square for Quadratics
To complete the square for the quadratic 2%2Ax%5E2-10%2Ax-168=0, we must first find a square which when expanded, has 2x2 and -10x in it.
Factoring 2 from the left side gives 2%28x%5E2-5%2Ax-84%29=0. %28x-2.5%29%5E2 is the square we are looking for. So we get 2%28%28x-2.5%29%5E2-90.25%29=0. Taking the -90.25 out of the 2, we get highlight%282%28x-2.5%29%5E2-180.5%29. Adding 180.5 to both sides, we get 2%28%28x-2.5%29%5E2%29=180.5. Dividing both sides by 2 gives %28x-2.5%29%5E2=90.25. Taking the square root of both sides gives system%28x-2.5=sqrt%2890.25%29=9.5%2Cx-2.5=-sqrt%2890.25%29=-9.5%29. system%28x=12%2Cx=-7%29 So the solutions are x=12 and x=-7.

Since the side lengths can't be negative, we discard x=-7, so x must be 12.
Therefore, the area is %282%2A12%29%2A12=highlight%28highlight_green%28highlight%28288%29%29%29 ft2.

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Mr.Ulep has a rectangular field with a length twice its width.
If 4 feet are taken from the length and 3 feet are taken from the width,
the area of the field is 180 square feet.Find the area of the original field
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Let x be the width; then the length is 2x.

The area equation is

    (2x-4)*(x-3) = 180,

or

    (x-2)*(x-3) = 90.

    x^2 - 5x + 6 = 90

    x^2 - 5x - 84 = 0

    (x+7)*(x-12) = 0


Of the two roots, x= -7  and  x= 12, only positive value x= 12 ft is the width.

Then the length is 2*12 = 24 ft.


ANSWER.  The area of the original rectangle is 12*24 = 288 ft^2.

Solved.


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The method shown by @shin123 is formally correct, but essentially is anti-pedagogical.

Solve simple problems using simple methods.