GRE Math Challenge Question #23
What is the length of side AB? Note: Figure NOT drawn to scale
A. 5 B. √30
C. 5√2
D. 8
E. 69
Solution:
Correct Choice: E
You are asked for the length of segment AB. For convenience, put the letter D on the point at the right angle between A and C;
Solve this multi-step problem by working backwards from your goal. To find the length of AB, you can use the Pythagorean theorem on triangle ADB, since angle ADB must be a right angle. In order to use the Pythagorean theorem, you need the lengths of the two legs. BD is known,
Finally, to find DC, apply the Pythagorean theorem to triangle BDC:
( √5)^2 + (DC)^2 = 32
5 + (DC)^2 = 9
(DC)^2 = 4
DC = 2
So AD = 10 - DC = 10 - 2 = 8. Apply the Pythagorean theorem to ADB:
( √5)2 + 8^2 = AB^2
5 + 64 = AB^2
AB = √69
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