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a square patio surrounded by a walkway of width x meters. If [#permalink]
17 Oct 2008, 08:36

a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkway, what is the area of the patio, in square meters?

I'm pretty sure that this is not an official GMAT question (which I will explain shortly) but here it goes:

Imagine a square (the patio) which is "framed" by a larger square (the walkway). x is the width of the walkway, so each side of the patio is x+5 meters long. The outer edges of the walkway will be (x+5)+x+x or simple 3x+5

The area of the larger, outer square MINUS the area of the patio will EQUAL the area of the walkway. So, our equation is (3x+5)^2 - (x+5)^2 = 132 If we simply this we get 8x^2 + 20x = 132 Set equal to zero to get 8x^2 + 20x - 132 = 0 Divide both sides by 4 to get 2x^2 + 5x - 33 = 0

Here's where I conclude that this is not an official GMAC question. Even though GMAC suggests that students need to know how to solve quadratics where the coefficient of the x^2 is not zero (and the quadratic is neither a square or a difference of squares) I have never seen an official question that tests this skill, and I've looked a lot of GMAT questions. That said, perhaps it is a real GMAT question (750+ level at that), so let's solve this quadratic. It's not that hard to factor.

Factor to get (x-3)(2x+11)=0 We get x=3 or x=some negative number. Since x must be positive, x must equal 3.

This means the sides of the patio are 8 meters long, which means the area of the patio is 64 square meters.

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