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XAT 2020 — QA & DI Question 1

Similarity of TrianglesEasy

Two lighthouses, located at points A and B on the earth, are 60 feet and 40 feet tall respectively. Each lighthouse is perfectly vertical and the land connecting A and B is perfectly flat. The topmost point of the lighthouse at A is A’ and of the lighthouse at B is B’. Draw line segments A’B and B’A, and let them intersect at point C’. Drop a perpendicular from C’ to touch the earth at point C. What is the length of CC’ in feet?

Answer & solution

  • A

    20

  • B

    30

  • 24

  • D

    The distance between A and B is also needed to solve this

  • E

    25

Solution

​​​​​​​

∆BAA’ ~ ∆BCC’
∴ BCBA=CC'AA'   …(1)

Also, ∆ABB’ ~ ∆ACC’
∴ ACAB=CC'BB'    …(2)

Adding (1) and (2) we get

AC+BCAB=CC'AA'+CC'BB' 

⇒ 1 = CC'AA'+CC'BB'

⇒ 1CC'=1AA'+1BB'

⇒ 1CC'=160'+140 = 124

∴ CC’ = 24.

Hence, option (c).

XAT 2020 QA & DI Q1: Two lighthouses, located at points A and B on the earth, are 60 feet and 40 feet tall respectively. Each light — Solution | TheCATExam