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RRB ALP 9th Aug 2018 shift-1 Question 16

Question 16

A ladder 13 m long reaches a window which is 12 m above the ground on side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 5m high, then the width of the street is:

Solution

Case 1- Length of ladder (BC) = 13m, Height of window above ground (AC) = 12m.

          By Pythagoras Theorem, $$AB^{2}+AC^{2}=BC^{2}$$

           Putting the values of AB, BC, AC in respective positions we get

          $$AB^{2}+12^{2}=13^{2}$$

          $$AB^{2}+144=169$$

           AB= 5m.

Case 2-

          Since the ladder is kept on the other side of the street so,

           Length of ladder (AE) = 13m, Height of window above ground (DE) = 5m.

          By Pythagoras Theorem, $$AD^{2}+DE^{2}=AE^{2}$$

          Putting the values of AE, DE, AD in respective positions we get AD= 12m.

Therefore, width of the street= $$AB+AD$$ =(5+12)m= 17m.



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