In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the

Question

similar triangle diagram.JPG In the diagram above, BD = 5, CD = 10, and AE = 40. What is the area of the shaded region? (A) 175 (B) 350 (C) 775 (D) 1150 (E) 1575 For a set of practice problems on Similar Geometric Figures, as well as the OE for this particular problem, see: https://magoosh.com/gmat/2014/gmat-pract ... c-figures/ Mike :-)

lolopolo · Answer

These are similar triangles, but small one is reversed. After noticing that, question is easily solved by proportion:
AE/BD=AC/CD=8/1

40*10*8/2 (area of big triangle) - 5*10/2 = 1575

Answer E

beattheheat · Answer

Triangle BCD is similar to Triangle ACE having one right angle and one common angle.
Ratio of sides is 1:8, thus ratio of Area will be 1:64.

Area of BCD = (5*10)/2= 25
Area of ACE = 64*(Area of BCD) = 64*25 = 1600

Area of shaded region = Area of ACE - Area of BCD = 1600 - 25 = 1575

Answer E

Akash777 · Answer

How do you know that Two triangles are in ratio 1 to 8? If you take CD to be as like side with AE, the two triangles will be in ratio 1 to 4.

m1033512 · Answer

IMO E

As the two trinagles are similar

(area of big triangle x )/(area of small triangle y) = (ratio of corresponding sides)^2

x/25 = (8/1)^2

x = 64*25 = 1600

so area of shaded region = 1600-25 = 1575

Award kudos if helpful

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TannyaChabbra · Answer

how do you conclude that they are similar triangles ? because either its SAS, AAA or SSS but here from the given question we know only one angle is equal? kindly help.

nick1816 · Answer

BDC=CAE ( both are 90*), BCD=ACE (common angle in 2 triangles)
Obviously remaining angles gonna be equal.

Fdambro294 · Answer

Triangle CAE ~ Triangle CDB

(by the A-A Postulate)

Ratio of Corresponding Sides:

Triangle CAE : Triangle CDB = Side AE : Side DB = 40 : 5 = 8 : 1

RATIO of Areas of Similar Triangles = SQUARE of the Ratio of Corresponding Sides in its most reduced form

AREA of Triangle CAE : AREA of Triangle CDB = (8)^2 : (1)^2 = 64 : 1

Actual Area of Triangle CDB = (1/2) * 5 * 10 = 25

Given the Ratio of Areas ----> Actual Area of Triangle ACE = 25 * (64) = 1, 600

Shaded Area = Area of Triangle ACE - Area of Triangle CDB = 1,600 - 25 =

1,575

-E-

Fdambro294 · Answer

I find it easier to remember the A-A-A Postulate to prove Triangle Similarity as just the

A-A Postulate

if 2 Angles are Equal across 2 Triangles ------> the 3rd Corresponding Angle will be Equal also and the Triangles will be Similiar

adityasuresh · Answer

Triangle ACE is similar to triangle BCD.

In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the

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GMAT Problem Solving (PS) Questions

In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the

Prep Toolkit

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