Problem Solving

In the figure below, if AC=12, DC=18, and DB=15, what is the length of AF?

A)8
B)9
C)10
D)11
E)12

Figure reference: https://24.media.tumblr.com/tumblr_m8gfp ... 1_1280.jpg

arifaisal wrote:In the figure below, if AC=12, DC=18, and DB=15, what is the length of AF?

A)8
B)9
C)10
D)11
E)12

Figure reference: https://24.media.tumblr.com/tumblr_m8gfp ... 1_1280.jpg

Hi arifaisal:

The quick way to do this is to recognize that the two right angled triangles :- AFC and BDC are similar. Hence their corresponding sides are proportional:

Then :
AF/BD = AC/DC
AF/15 = 12/18
=> AF = 2/3 * 15 = 10

C is correct

arifaisal wrote:In the figure below, if AC=12, DC=18, and DB=15, what is the length of AF?

A)8
B)9
C)10
D)11
E)12

Any side of a triangle can be deemed the base.
Each base has a corresponding height.
No matter which base and height are used, the area of the triangle must be the same value.
Thus, regardless of which side of a triangle is deemed the base, bh must always yield the same product.



In triangle ADC:
If AC is deemed the base, then BD is the corresponding height.
If CD is deemed the base, then AF is the corresponding height.
Since bh must yield the same product no matter which base and height are used, we get:
(AC)(BD) = (CD)(AF)
12*15 = 18(AF)
AF = 10.

The correct answer is C.