PS - Triangle %percent

[karthikpandian19]

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

[Anurag@Gurome]

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.

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.

[karthikpandian19]

Anurag,

the Correct answer is [spoiler]8 (D)[/spoiler]

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.

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.

[Anurag@Gurome]

the Correct answer is [spoiler]8 (D)[/spoiler]

Sorry.
I made a mistake.
Edited my post.

[padhyajay5]

Easy enough...but nice problem..!!