Question

Adjoining figure depicts a racing track whose left and right ends are semicircular. The distance between two inner parallel line segments is 70 m and they are each 105 m long. If the track is 7m wide, find the difference in the lengths of the inner edge and outer edge of the track.

Answer 1

Given:
Distance between two inner parallel line segments = 70 m
Length = 105 m
Width of the track = 7 m
∴ Distance between two outer parallel line segments = 70 m + 7 m + 7 m = 84 m
Also,
Radius of the inner semicircle = $\frac{70}{2}$ m = 35 m
Radius of the outer semicircle = (35 + 7) m = 42 m
Length of the inner edge of the track = (2 × Distance between the two inner semicircular paths + 2 × Circumference of the inner semicircle)
= 2 × 105 + 2 × $\frac{22}{7}$ × 35 m
= (210 + 220) m
= 430 m
Similarly,
Length of the outer edge of the track = (2 × Distance between the two outer semicircular paths + 2 × Circumference of the outer semicircle)
= 2 × 105 + 2 × $\frac{22}{7}$ × 42 m
= (210 + 264) m
= 474 m

∴ Difference in the lengths of the inner and outer edges of the track = 474 m $-$ 430 m = 44 m