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.

• 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
• 10 years agoHelpfull: Yes(0) No(0)
• 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
• 9 years agoHelpfull: Yes(0) No(0)