Bunuel wrote:

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Rectangle ABCD is inscribed in a circle with center X. If the area of the rectangle is eight times its width, and the distance from X to side AB is three, what is the approximate circumference of the circle?

A. 5

B. 10

C. 30

D. 45

E. 75

Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTION:The correct response is (C). To find the circumference of a circle, we must find the radius. Let’s start with what we know:

The area of a rectangle is lw. Here we are told that lw = 8w. That means the length is 8. We also know that from X to AB =3, so the length of the rectangle must be 6. Let’s re-draw the shape:

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We can see that a right triangle is formed with the radius AX and half the length and width of the rectangle. Since it’s a classic Pythagorean triplet (3:4:5), we don’t need to use the Pythagorean theorem!

Now that we have the radius, we can plug it into the formula for circumference: C=2πr. C=2∗π∗5. The circumference is approximately 10π, or a number slightly larger than 30.

If you chose (A), you correctly found the radius, but stopped short of finding the circumference. Remember to write down what the question is asking you, especially for this type of multi-step problem, so you don’t stop half-way there!

If you chose (B), the circumference is 10π, but since the question asks for an approximate answer and each choice omits π, you’ll need to multiple 10 by 3 to get the right choice, answer (E).

If you chose (D), this approximation is too large. Even if you were worries that 30 was too small, remember that π = about 3.14. Multiplying is by 10 will only move the decimal one place to the right, giving us 31.4, a number still much closer to (C) than 45.

If you chose (E), you correctly found the radius, but then calculated the approximate area (πr^2) and not the approximate circumference. Review both formulas to make sure you don’t get them mixed up on the GMAT!

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