Ayush starts walking from his house to office . Instead of going to the office directly , he goes to bank first , from there to his daughter 's school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office ? (Assume that all distance covered are in straight lines ). If the house is situated at (2,4) bank at (5,8), school at (13,14) and office at (13,26) and coordinates are in km.

Explanation

Consider the co-ordinates of house, H(2, 4), bank, B(5, 8), school, S(13, 14) and office, O(13, 26).
`" ""Distance "HB^(2)=(5-2)^(2)+(8-4)^(2)=3^(2)+4^(2)=9+16=25`
`rArr" "HB=5" km"`
`" "` Distance `BS^(2)=(13-5)^(2)+(14-8)^(2)=8^(2)+6^(2)=64+36`
`rArr" "BS^(2)=100`
`rArr" "BS=10" km"`
Distance `" "SO^(2)=(13-13)^(2)+(26-14)^(2)=0^(2)+12^(2)=12^(2)`
`rArr" "SO=12" km"`
Total distance travelled by Ayush from house to bank to school and then to office
`" "=HB+BS+SO=5+10+12=27" km"`
Direct distance from house to office =HO
`rArr" "HO^(2)=(13-2)^(2)+(26-4)^(2)=(11)^(2)+(22)^(2)`
`rArr" "HO^(2)=121+484`
`rArr" "HO=sqrt(605)=24.6" km"`
So, extra distance travelled by Ayush = 27 km- 24.6 km = 2.4 km.
Hence, extra distance travelled by Ayush = 2.4 km.