Geometry, Distance and Ratio Problem, Please Help

[bretania]

56.
When a certain projector is 4 feet from the wall, the area of the picture on the wall is 9 square feet. If the projector is moved to a position n times as far away from the wall, then the picture will take up n^2 times as much space on the wall. If the projector is 6 feet from the wall, what is the area, in square feet, of the picture on the wall?

A. 2
B. 8/3
C. 27/2
D. 18
E. 81/4

[Crack_Mat]

Is the answer C?

[Crack_Mat]

Sorry I miss calculated ....answer should be E.

Here is my approach:

4 F --------9 Sq F

Now moved to 4*n distance and area is n^2 * 9
as area increase on increasing distance, they are directly proportional.

So if n = 6/4?
4* 6/4 ---------------(6/4)^2 * 9 = (3/2)^2 * 9 = 81/4

Please tell us the answer bretania.

[bretania]

Yes, the answer here is E.
Sorry I just noticed this now.

[Naimish Patel]

projector moved from 4 to 6.
so 6/4=1.5

so projector is moved 1.5 times so area will be square of 1.5=2.25

so original area was 9 sq.ft x 2.25 = 20.25=21

hence answer is E