ABCD is a rectangle if unshaded area is 48 cm2 and AB:BC=3:2. find the perimeter of rectangle. sORRY NO FIGURE; Shaded region: Triangle BEC and Triangle AED Unshaded region: Triangle BEA and Triangle CED
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GMAT Club Forum Index Data Sufficiency (DS)
Given that ABCD is a rectangle, is the area of triangle ABE> : Data Sufficiency (DS)
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Difficulty: 700-Level
Topic Discussion
Page 1 of 1
enigma123 Feb 4, 2012
00:00 ABCDE
DIFFICULTY: 65% (hard) QUESTION STATS: based on 608 sessions
58% (01:51) correct
42% (01:45) wrong
Given that ABCD is a rectangle, is the area of triangle ABE > 25?
(Note: Figure above is not drawn to scale).
Rectangle.PNG
Rectangle.PNG (2.86 KiB) Viewed 45063 times
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(1) AB = 6
(2) AE = 10
How come the answer is B and not C? Can someone please explain?
PS: I tried the jpeg and bitmap format to attach the picture, but it says these two formats are not supported. Therefore attached the .pdf.
Spoiler: OA
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Most Helpful Expert Reply
Bunuel
EXPERT'S
POST
Feb 4, 2012
Given that ABCD is a rectangle, is the area of triangle ABE > 25? (Note: Figure above is not drawn to scale).
Rectangle.PNG
Rectangle.PNG (2.86 KiB) Viewed 44955 times
Open
Area=12∗AB∗BEArea=12∗AB∗BE
(1) AB = 6 --> clearly insufficient: BE can be 1 or 100.
(2) AE = 10 --> now, you should know one important property: for a given length of the hypotenuse a right triangle has the largest area when it's isosceles, so for our case area of ABE will be maximized when AB=BE. So, let's try what is the largest area of a right isosceles triangle with hypotenuse equal to 10. Finding legs: x2+x2=102x2+x2=102 (where x=AB=BE) --> x=50−−√x=50 --> areamax=1250−−√2=25areamax=12502=25. Since it's the maximum area of ABE then the actual area cannot be more than 25. Sufficient.
