Question 423350: The area of a rectangle field is 9x^2 - 6xy + y^2 sq units. Find Expressions for length and breadth of the field. When x=12 units and y=6 units please evaluate length and breadth.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! area is equal to:
9x^2 - 6xy + y^2
this would be factored as:
(3x-y) * (3x-y)
multiply these factors out and you get 9x^2 - 6xy + y^2 which is the original equation.
when x = 12 and y = 6, this becomes:
(36-6) * (36-6) = 30*30 = 900 square units.
plug those values into the original equation:
9x^2 - 6xy + y^2 becomes 9*12^2 - 6*12*6 + 6^2 becomes 9*144 - 12*36 + 36 becomes 1296 - 432 + 36 becomes 900.
you get the same answer, as you should.
the rectangle field is really a square.
you get this from the fact that (3x-y) * (3x-y) = area of the field.
since the area of a rectangle is length * width, then:
the length is 3x-y and the width is 3x-y.
when x = 12 and y = 6, this comes out to a length of 30 and a width of 30.
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