Latest self Aptitude Question SOLUTION: Shamu has to get home from his school to do some chores for his mother. The distance between the house and school is 3km if he walks along a straight line. Instead Shamu decides to

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(#M40030757) SELF question Longest Path Keep an EYE

Shamu has to get home from his school to do some chores for his mother. The distance between the house and school is 3km if he walks along a straight line. Instead Shamu decides to go along two line segments to reach home such that, throughout his route , he is getting closer to home. What is the length (in km) of the longest route he can take? The figure below shows a valid and an invalid route that Shamu can take.

Alok (10 years ago)

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anitha  (10 years ago)

To saisfy the condition "Instead Shamu decides to go along two line segments to reach home such that, throughout his route , he is getting closer to home" he must walk alon two mutually perpendicular paths
Let the length of one segment be 'x' and other 'y'
Hence x²+y²=3²=9
Maximise z=x+y
x²+y²=9
→ x²=9 −y²
→x=√(9 −y²)
z=x+y
→ z=√(9 −y²)+y
→dz/dy= {1/{2√(9 −y²)}]×(−2y)+1
= −y/√(9 −y²)+1
For z to be maximum or minimum dz/dy=0 →−y/√(9 −y²)}+1=0
i.e −y/√(9 −y²)}=−1
Hence either y= √(9 −y²)
i.e y² =(9 −y²)
0r 2y² =9 an y= √(9/2) =3√2/2
hence x= √(9 −y²) =√(9 −9/2) =3√2/2
Hence maximum distance = 3√2/2+3√2/2=3√2

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Manikanta  (9 years ago)

Shamu has to get home from his school to do some chores for his mother. The distance between the house and school is 3km if he walks along a straight line. Instead Shamu decides to go along two line segments to reach home such that, throughout his route , he is getting closer to home. What is the length (in km) of the longest route he can take? The figure below shows a valid and an invalid route that Shamu can tak

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