SAT Math Question

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1

<p>Hey everyone..Just curious on how you would approach this question that can be found in the Official SAT Study Guide book Second Edition (page 519, question 20)*:</p>

<p>At a beach, a rectangular swimming area with dimensions x and y meters and a total area of 4000 square meters is marked off on three sides with rope, as shown above*, and bounded on the fourth side by the beach. Additionally, rope is used to divide the area into three smaller rectangular sections. In terms of y, what is the total length, in meters, of the rope that is needed both to bound the three sides of the area and to divide it into sections?</p>

<p>A) y + 4000/y
B) y + 16000/y
C) y + 16000/3y
D) 3y + 8000/3y
E) 3y + 16000/3y</p>

<p>The answer is <strong>B</strong>, but am perplexed as how to figure it out. Any help would be greatly appreciated.</p>

2

<p>I usually plug in numbers. It’s a little hard to answer this because I can’t picture the image in my head.</p>

3

<p>It’s pretty simple, actually. I checked the figure, and here’s the answer:
So you have 5 ropes lining the rectangle, the beach doesn’t count. So the total length of the rope is 4x + y since you have 4 lengths of x and one length of y. The area is 4000, so that means that xy=4000. They want it all in terms of y, so find x in terms of y. Using the area equation: xy = 4000 => x=4000/y. Now just replace into the equation of the rope length: 4x+y = 4(4000/y) + y = 1600/y + y, which is choice B. </p>

<p>Plugging in numbers could get you there I suppose, but it takes too much more time.</p>