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Since we are given that E is the midpoint of AC then AE and EC are same.

We know that when the two bases are same the areas of triangles are also same..i.e.e 24 = 12+12 for two triangles.

Now BEC triangle is 12..

In BEC = BED + EDC triangles = 12.. we can happily discard option C because BED has to be lesser than 12...

From options we can say that BED area given then we can apply our logic.

A) 9 *1.7 = 15.3 which is greater than 12...not correct B) 9*1.4 = 12.6 > 12...not correct D) can be E) 6*1.4/1.7 ~ 4.6... we can say from the shaded region BED is greater than EDC and this can't be the option.

E is the midpoint of AC in right triangle ABC shown above. If the area [#permalink]

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22 Sep 2016, 07:06

I have D as well:

1) Area of total triangle is 24. BE is the median of side AC and divides the triangle in 2 triangles of area 12. 2) Since the triangle ABC is right and isosceles with angles 45-45-90, and we know that area is 24, we know the length of the sides is 4*sqrt(3) 3) Since BE splits AC in half, we know that the length of EC is 2*sqrt(3), and as we have again a 45-45-90 triangle, ED is 2*sqrt(3)/sqrt(2), simplify to sqrt (6) 4) Area of EDC is therefore (sqrt(6)^2)/2 = 3 5) Area of BED is 12 -3 = 9

Re: E is the midpoint of AC in right triangle ABC shown above. If the area [#permalink]

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23 Sep 2016, 08:56

Azamaka, are you sure that AEB=BED? since BE is the median of AC, it should split the are of triangle ABC in half, so AEB=BCE not BED - or is there something I am missing?

E is the midpoint of AC in right triangle ABC shown above. If the area [#permalink]

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26 Sep 2016, 02:23

Bunuel wrote:

E is the midpoint of AC in right triangle ABC shown above. If the area of ΔABC is 24, what is the area of ΔBED?

After getting ΔBEC to be 12 units, I assumed for a moment ED to be of 1 unit. I did this only to work out the ratio. ED=DC=1. So, EC = sqrt2. AC=2(sqrt2). Because angle C is 45, AB=AC=2(sqrt2). Hypotenuse BC = 4 = BD+DC (DC =1, as mentioned above) BD=3. Finally, the ration of ΔBDE and ΔEDC will be in the ratio if 3:1 because they have a common height of ED. Divide 12 in the ratio and 9 is the answer for the shaded region.

Re: E is the midpoint of AC in right triangle ABC shown above. If the area [#permalink]

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15 Dec 2017, 14:07

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