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M and N start from the same location. M travels 10 km East and then 10 km North-East. N travels 5 km South and then 4 km South-East. What is the shortest distance (in km) between M and N at the end of their travel.
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- 18.60
- 22.50
- 20.61
- 25.00
Correct Option: C
From the given data, the following diagram is possible 
| cos 45° = | ||
| 4 |
DE = cos45° × 4 = 2.828 km
| sin 45° = | ||
| 4 |
EN = sin 45° × 4 = 2.828 km
| sin 45° = | ||
| 4 |
EN = sin 45° × 4 = 2.828 km
CN = NE + CE = 2.828 + 5 = 7.828 km
CB = AB – AC = 10 – 2.828 = 7.171 km
(NB)² = (NC)² + (BC)²
= (7.828)² + (7.171)²
∴ NB = √(7.828)² + (7.171)²
= 10.616 km
∴ NM = NB + BM = 10.616 + 10
= 20.61 km
