Find the ratio of areas of the Triangle ABC and ADB

Question

Find the ratio of areas of the triangle ADB and ABC. If BD:DC = 3:5

A. 3:5
B. 9:25
C. 3:8
D. 5:9
E. 9:16

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Bunuel · Answer

BD:DC = 3:5 --> BD:(BD+DC) = 3:(3+5) --> BD:BC = 3:8.

The area of triangle ADB = 1/2*(height from A to DB)*(DB).
The area of triangle ABC = 1/2*(height from A to BC)*(BC).

Notice that (height from A to DB) = (height from A to BC).

Therefore the ration of the areas of ADB and ABC = DB:BC = 3:8.

Answer: C.

sunita123 · Answer

Hi Bunuel,
Excuse me if i do not have clear concept in Geometry.

So I do not understand how below statement is true.

(height from A to DB) = (height from A to BC).

Thanks for your help.

Bunuel · Answer

Line segments DB and BC are on the same line, thus the perpendicular from point A to DB is the same as the perpendicular from point A to BC.

ronr34 · Answer

Hi Bunuel,

in a lot of questions, we get to the bottom line of: ratio of area = (ratio of side)^2.

Is this not true? Is this true only in specific cases?

Bunuel · Answer

This is true for similar triangles.

If two similar triangles have sides in the ratio  \frac{x}{y} , then their areas are in the ratio  \frac{x^2}{y^2} .
OR in another way: in two similar triangles, the ratio of their areas is the square of the ratio of their sides:  \frac{AREA}{area}=\frac{SIDE^2}{side^2} .

mvictor · Answer

oh damn..i was on my laptop..and the screen is small...i did not see the image..was going crazy to identify how the triangle might look like...
BD= suppose 3x
DC = 5x
BC=8x
the height is the same for the both triangles, so basically, we are asked for the ratio of the bases. BC/BD = 3x/8x = 3/8

CEdward · Answer

Bunuel

I am confused. So this current problem, the triangles are not similar?

Bunuel · Answer

No, there are no similar triangles in the figure.

rsrighosh · Answer

I too fell in the trap thinking that these are similar triangles.... and I was making a mistake of drawing the 2 perpendicular lines 1 from D and the other from C

But perpendicular from A makes more sense. Answer is indeed 3/8

Bunuel  Thanks a lot

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Find the ratio of areas of the Triangle ABC and ADB

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Find the ratio of areas of the Triangle ABC and ADB

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