Daily Regents: Quadratic Equations with Area (August 2016)

I'll be reviewing a New York State Regents Exam Question every day from now until the Regents exams begin next month. At least, that is the plan.

August 2014, Questions 36

36. A school is building a rectangular soccer field that has an area of 6000 square yards. The soccer field must be 40 yards longer than its width. Determine algebraically the dimensions of the soccer field, in yards.

Area of a rectangle is L * W. This is important: this formula will NOT be given to you because they assume you learned it in or before middle school. Seriously: it's A = L* W.

The width of the field can be called W. That means that the length is 40 more than the width, so L = W + 40.
The Area = L * W = W(W + 40) = 6000.

Distribute the W, and you get W² + 40W = 6000
Subtract 6000 from both sides: W² + 40W - 6000 = 0. You have a quadratic equation that needs to be factored.

The factors of -6000 with a sum of +40 are 100 and -60.
So (W + 100)(W - 60) = 0
Then W + 100 = 0 or W - 60 = 0
And W = -100 or W = 60.

Because we are looking for width, we can discard the negative value, and use the positive value. The width is 60. The length is 60 + 40 = 100.

Any questions?

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