A running track has 2 semicircular ends of radius 63 m and two straight lengths. The perimeter of the track is 1000 m. Find each straight length.
Solution:
The running track basically consists of a rectangle with two semi-circles at both ends as evident from the diagram below:
The perimeter of the track shown above is 1000m. Therefore we can write
L + L + πr + πr = 1000 ( Circumference of semicircle = 2πr/2= πr)
r = 63m
2L + (22/7) × 63 + (22/7) × 63 = 1000
2L + 198 + 198 = 1000
2L + 396 = 1000
2L = 1000 - 396 = 604
2L = 604
L = 302
The straight lengths = 302 m each
✦ Try This: A running track has 2 semicircular ends of radius 49 m and two straight lengths.
The perimeter of the track is 800 m. Find each straight length.
The running track basically consists of a rectangle with two semi-circles at both ends as evident from the diagram below:
The perimeter of the track shown above is 800 m. Therefore we can write
L + L + πr + πr = 800 ( Circumference of semicircle = 2πr/2= πr)
r = 49m
2L + (22/7) × 49 + (22/7) × 49 = 800
2L + 154 + 154 = 800
2L + 308 = 1000
2L = 1000 - 308 = 692
2L = 692
L = 346
The straight lengths = 302 m each
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 71
A running track has 2 semicircular ends of radius 63 m and two straight lengths. The perimeter of the track is 1000 m. Find each straight length.
Summary:
A running track has 2 semicircular ends of radius 63 m and two straight lengths. The perimeter of the track is 1000 m. Each straight length is 302m
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