the rectangle abcd represent a park the lines show all the paths in the park the circular path is in the center of the rectangle and has a diameter of 10m. Calculate the shortest distance from A to c across the park, using only the paths shown
Answers
Given : the rectangle abcd represent a park the lines show all the paths in the park the circular path is in the center of the rectangle and has a diameter of 10m.
To Find : the shortest distance from A to c across the park, using only the paths shown
Solution:
One path via B = AB + BC = 50 + 80 = 130 m
One path via D = AD + DC = 80 + 50 = 130
One path via diagonal and circle
Diagonal = √(50)² + (80)² = 94.34 m
Diameter of circle = 10 m to be subtracted and circumference of semi circle to be added as person has to go through boundary of circle only
circumference of semi circle = π(radius) = 3.14 * (10/2) = 15.7 m
Hence Distance = 94.34 - 10 + 15.7
= 100.04
≈ 100 m
the shortest distance from A to c across the park ≈ 100 m
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