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Question
Jayanti takes shortest route to her home by walking diagonally across a rectangular park. The park measures 60 metres × 80 metres. How much shorter is the route across the park than the route around its edges?
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Solution
As the park is rectangular, all the angles area of 90°
In right angled ΔABC,
AC2 = AB2 + BC2 ...[By Pythagoras theorem]
⇒ AC2 = (60)2 + (80)2 = 3600 + 6400
⇒ AC2 = 10000
⇒ AC = `sqrt(10000)`
⇒ AC = 100 m
If she goes through AB and AC, then the total distance covered = (60 + 80) m = 140 m
∴ Difference between two paths = (140 – 100) m = 40 m.
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