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Question #1: If a · b = 18 and a / b = 2, a > 0, b > 0 then:
(a) a = 18 and b = 1
(b) a = 9 and b = 2
(c) a = 18 and b = 9
(d) a = 6 and b = 3
(e) a = 6 and b = 6
Answer: a / b = 2
a = 2·b.
a·b = (2· b)· b
a·b = 2· b 2.
2· b 2 = 18
b 2 = 9,
b = 3 because b > 0,
a = 2· b
a = 6.
Question #2: The ratio of the radii of two circles is r1/r2 = 6. What is the ratio of the perimeters P1/P2 and the ratio of the areas of the two circles A1/A2?
(a) perimeter ratio = 1/6, area ratio = 36
(b) perimeter ratio = 36, area ratio = 6
(c) perimeter ratio = 6, area ratio = 36
(d) perimeter ratio = 1/8, area ratio = 8
(e) perimeter ratio = 1/6, area ratio = 6
Answer: r1 / r2 = 6;
Perimeter1 / Perimeter2 = (2· ¶· r1)/(2· ¶· r2) = r1/ r2 = 6
Area1 / Area2 = (¶· r12)/ (¶· r22) = r12 / r22 = 36
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