Hi maakya,
First name the point on the diagonal, E. Now we can see that the triangle BCE and the triangle BCD are similar, since BC is in both triangles and both triangles have the angle that is equal to 90.
EC/CD = BC/BD = BE/BC
EC/15 = 20/25= BE/20
EC = 12, BE = 16
Therefore,
Area = EC.BE/2 = (16).(12)/2 = 96
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Area of Shaded Region
Source: Beat The GMAT — Problem Solving |
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IMPORTANT: the diagrams in problem solving questions are DRAWN TO SCALE unless stated otherwise.
If ABCD is a rectangle, what is the area of the shaded region?
A) 64
B) 82
C) 96
D) 120
E) 150
So, even though this is a tricky question, we can quickly eliminate 3 of the answer choices and have a 50-50 chance of guessing correctly. Here's how:
Rectangle ABCD has dimensions 15 x 20, so its area = 300.
So, the area of ∆BCD = 150 (half of 300)
So, the shaded area must have an area that's LESS THAN 150
So, we can eliminate E
Answer choices A and B are both APPROXIMATELY half of 150.
Does it look like half of ∆BCD is shaded?
NO.
So. we can eliminate A and B.
This leaves us with a guess between C and D
FINAL NOTE: The diagram provided here is obviously not drawn to scale, so unless there's some missing text (saying "not drawn to scale") that was supposed to accompany the diagram , this is not a GMAT-quality question.
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
