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Complete Question:
ABCD Is a rectangle that represents a park.
The lines show all the paths in the park.
The circular path is in the centre of the rectangle and has a diameter of 15m.
Calculate the shortest distance from A to C across the park,using only the lines shown.
*See attachment for the diagram showing the paths in the park.
Answer:
Shortest distance from A to C through the paths only = 102.9 m
Step-by-step explanation:
Length of park = 80 m
Width of park = 50 m
Diameter of the circular path in the center of the park = 15 m
Therefore:
Shortest distance between from A to C across the park if we're to follow only the lines showing the oaths would be = (length of diagonal AC - diameter of the circular path) + (½ of the circumference of the circular path)
✔️Use pythagorean theorem to find AC:
AC = √(80² + 50²) = √8,900
AC = 94.3398113 ≈ 94.34 m (nearest hundredth)
✔️Diameter of circular path = 15 m
✔️½ of the circumference of the circular path = ½(πd)
d = 15 m
½ of the circumference = ½(π*15) = 23.5619449 ≈ 23.56 m (nearest hundredth)
✔️Shortest distance = (94.34 - 15) + 23.56 = 79.34 + 23.56 = 102.9 m
