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# 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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