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If points A and B are 5 units apart, which of the following

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If points A and B are 5 units apart, which of the following

by BTGmoderatorAT » Mon Dec 18, 2017 4:58 pm
If points A and B are 5 units apart, which of the following can have only one possible value?

I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

OA: A

I'm confused how to set up the formulas here. Can any experts show?
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by [email protected] » Mon Dec 18, 2017 8:58 pm
Hi ardz24,

We're told that points A and B are 5 'units' apart (and we're meant to assume that a 'unit' is a fixed measurement - NOT a variable). We're asked which of the following can have ONLY ONE possible value. This is a great 'concept question', meaning that you don't have to do much math to answer it IF you understand the concepts involved.

I. The area of a square region with side AB

Roman Numeral 1 refers to a SQUARE, so we know that all 4 sides are equal and the area = (side)^2. With a length of 5 units, the area MUST be (5)^2 = 25 units. There is no other possible value. Eliminate Answers B and C.

II. The circumference of a circle passing through points A and B

Roman Numeral 2 refers to the two points (A and B) being on the circumference of the circle. As such, the circumference could have LOTS of different values. For example, the length AB could be the diameter of the circle OR it could be ANY other chord on the circle (which would make the circumference BIGGER than if AB was the diameter. Eliminate Answer D.

III. The area of a rectangular region with diagonal AB

Roman Numeral 3 refers to the diagonal of a rectangle. That diagonal could be from ANY rectangle that fits the equation X^2 + Y^2 = 5^2. The sides of the rectangle could be 3 and 4 (so the area would be 12) or they could be 1 and (root24) (so the area would be root24). Thus, there are multiple possible areas. Eliminate Answer E.

Final Answer: A

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