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PS - Triangle %percent

by karthikpandian19 » Mon Jul 16, 2012 10:53 pm
Please explain the easy way to do the problem:


Juan is 6 feet tall. When he is a certain distance away from a street lamp that is 30 feet tall, he casts a shadow as long as he is tall. How many feet further does he need to stand from the base of the street lamp in order for his shadow to be 33.333% longer than it is now?


(A) 2

(B) 5

(C) 6

(D) 8

(E) 10
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by Anurag@Gurome » Mon Jul 16, 2012 11:14 pm
karthikpandian19 wrote:Juan is 6 feet tall. When he is a certain distance away from a street lamp that is 30 feet tall, he casts a shadow as long as he is tall. How many feet further does he need to stand from the base of the street lamp in order for his shadow to be 33.333% longer than it is now?
In the following diagram, the blue line is the street lamp, the red line is Juan, and the green line is the shadow.
Image
Triangle ABC and triangle APQ are similar triangles.
Hence, AP/PQ = AB/BC
Hence, AB = BC*(AP/PQ) = 30*AP/6 = 5*AP
Hence, the distance = PB = (AB - AP) = (5*AP - AP) = 4*AP = 4*(Shadow length)

In the first case,
  • Shadow length = Juan's height = 6 feet
    Hence, d = 4*6 = 24 feet
In the second case,
  • 33.333% = 1/3
    Hence, length of new shadow = (6 + 6/3) feet = 8 feet
    Hence, d = 4*8 = 32 feet
Hence, difference in distance = (32 - 24) = 8 feet

The correct answer is D.
Last edited by Anurag@Gurome on Mon Jul 16, 2012 11:54 pm, edited 1 time in total.
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by karthikpandian19 » Mon Jul 16, 2012 11:46 pm
Anurag,

the Correct answer is [spoiler]8 (D)[/spoiler]
Anurag@Gurome wrote:
karthikpandian19 wrote:Juan is 6 feet tall. When he is a certain distance away from a street lamp that is 30 feet tall, he casts a shadow as long as he is tall. How many feet further does he need to stand from the base of the street lamp in order for his shadow to be 33.333% longer than it is now?
In the following diagram, the blue line is the street lamp, the red line is Juan, and the green line is the shadow.
Image
Triangle ABC and triangle APQ are similar triangles.
Hence, AP/PQ = AB/BC
Hence, the distance d = AB = BC*(AP/PQ) = 30*AP/6 = 5*AP = 5*(Shadow length)

In the first case,
  • Shadow length = Juan's height = 6 feet
    Hence, d = 5*6 = 30 feet
In the second case,
  • 33.333% = 1/3
    Hence, length of new shadow = (6 + 6/3) feet = 8 feet
    Hence, d = 3*8 = 40 feet
Hence, difference in distance = (40 - 30) = 10 feet

The correct answer is E.
Regards,
Karthik
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by Anurag@Gurome » Mon Jul 16, 2012 11:55 pm
karthikpandian19 wrote:the Correct answer is [spoiler]8 (D)[/spoiler]
Sorry.
I made a mistake.
Edited my post.
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by padhyajay5 » Tue Jul 17, 2012 7:21 am
Easy enough...but nice problem..!!
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