Ashok wants to go by a car from village A to B.he can (i)go straight from A to B(ii)first go to C due east and then from C to B due north.the distance between A and B exceeds the distance between A and C by 9 km. the distance between A and B is 9km less than twice the distance between B and C. Ashok decides to go straight from A to B. Find the distance between (i) A and B (ii) A and C (iii) C and B
Answers
Given : Ashok wants to go by a car from village A to B.he can
(i) go straight from A to B
(ii) first go to C due east and then from C to B due north.
the distance between A and B exceeds the distance between A and C by 9 km.
the distance between A and B is 9km less than twice the distance between B and C.
To Find : distance between (i) A and B (ii) A and C (iii) C and B
Solution:
Distance between AC = x km
=> Distance between AB = x + 9
2 ( BC) - 9 = x + 9
=> 2 (BC) = x + 18
=> BC = x/2 + 9
AC² + BC² = AB²
=> x² + (x/2 + 9)² = (x + 9)²
=> x² + x²/4 + 9x + 81 = x² + 18x + 81
=> x²/4 = 9x
=> x/4 = 9
=> x = 36
Distance between AC = 36 km
Distance between AB = 36 + 9 = 45 km
Distance between BC = x/2 + 9 = (36/2) + 9 = 27 km
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