SOLUTION: A rectangular painting with a width of x centimeters has an area of x^2+50x square centimeters. Find a binomial that represents the length.

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Question 78608This question is from textbook Elementary and Intermediate Algebra
: A rectangular painting with a width of x centimeters has an area of x^2+50x square centimeters. Find a binomial that represents the length. This question is from textbook Elementary and Intermediate Algebra

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the area of a rectangle is A = L*W in which A represents the Area, L is the
Length and W is the width.
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The problem states that the Area is given by x%5E2+%2B+50x and the Width is x.
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Substitute these two values into the area formula and you get:
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x%5E2+%2B+50x+=+L%2Ax
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To solve for L, divide both sides of this equation by x, the multiplier of L and you get:
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%28x%5E2+%2B+50x%29%2Fx+=+L
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Divide the x of the denominator into each of the two terms in the parentheses and the
result is:
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x%5E2%2Fx+%2B+50x%2Fx+=+L
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recall that x%5E2+=+x%2Ax so dividing x^2 by x is the same as x%2Ax%2Fx and the x
in the denominator cancels with one of the x's in the numerator. So the result is of
this division is just x. Similarly, when you divide 50x by x the x in the
denominator cancels the x in the numerator. Therefore, this division just results in
50. So when these divisions are performed the equation simplifies to:
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x+%2B+50+=+L
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and this is the binomial you were asked to find:
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L+=+x+%2B+50
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and when you solve for L, don't forget that the answer is in centimeters.
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Hope this helps you to understand the problem a little better.