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)   (Show Source): You can put this solution on YOUR website!
Since the length is twice the width, let's say the length is and the width is . So we have the equation . Expanding, we get .
Solved by pluggable solver: Completing the Square for Quadratics
To complete the square for the quadratic , we must first find a square which when expanded, has 2x2 and -10x in it.
Factoring 2 from the left side gives . is the square we are looking for. So we get . Taking the -90.25 out of the 2, we get . Adding 180.5 to both sides, we get . Dividing both sides by 2 gives . Taking the square root of both sides gives . So the solutions are x=12 and x=-7.

Since the side lengths can't be negative, we discard , so x must be 12.
Therefore, the area is ft2.
Answer by ikleyn(52794)   (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
~~~~~~~~~~~~~~~~~~ 

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.



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