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| Math Central | Quandaries & Queries |
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Question from bill, a student: The area of the rectangle is 170 sq.ft. the width is unknown and the length is the width plus 7 ft. |
Hi Bill,
With w(w + 7) = 170 the next step should be to expand the left side. Using the dissimulative law
w(w + 7) = w × w + w × 7 = w2 + 7w
Hence you have
w2 + 7w = 170
Next subtract 170 from each side
w2 + 7w - 170 = 170 - 170
w2 + 7w - 170 = 0.
The task now is to factor w2 + 7w - 170, that is to find numbers a and b so that
w2 + 7w - 170 = (x + a)(x + b)
Notice that if you expand the right side you get
(x + a)(x + b) = x2 + (a + b)x + ab
Hence to have
w2 + 7w - 170 = (x + a)(x + b) = x2 + (a + b)x + ab
you want numbers a and b so that ab = 170 (so one is positive and one is negative) and a + b = 7.
Can you find a and b and complete the problem?
If you need further assistance write back,
Penny
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