CAMANISHPARMAR wrote:
In the figure above, the measure of angle EAB in triangle ABE is 90 degrees, and BCDE is a square. What is the length of AB?
(1) The length of AE is 12, and the ratio of the area of triangle ABE to the area of square BCDE is \(\frac{6}{25}\).
(2) The perimeter of square BCDE is 80 and the ratio of the length of AE to the length of AB is 3 to 4.
Always look for SPECIAL TRIANGLES.
Statement 1:Since the length of AE is divisible by 3 and 4, test whether it's possible that ABE is a multiple of a 3:4:5 triangle.
Case 1: AE=12, AB=16 and BE=20, with the result that AE:AB:BE = 3:4:5
In this case:
\(\frac{ABE}{BCDE} = \frac{(0.5 * 12 *16)}{20^2} = \frac{96}{400} = \frac{6}{25}\).
Case 2: AE=12, AB=9 and BE=15. with the result that AB:AE:BE = 3:4:5
In this case:
\(\frac{ABE}{BCDE} = \frac{(0.5 * 12 * 9)}{15^2} = \frac{54}{225} = \frac{6}{25}\).
Statement 1 is satisfied by both cases.
Since AB can be different values, INSUFFICIENT.
Statement 2:Statement 2 is satisfied only by Case 1.
Thus, AB=16.
SUFFICIENT.
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