Question

ABCD is a rectangle that represents 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 15

Answer 1

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