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mikemcgarry
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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.
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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


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

TannyaChabbra
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.
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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-
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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


TannyaChabbra
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.
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Triangle ACE is similar to triangle BCD.
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