Question

The inside perimeter of a running track (shown in Fig.) is 400 m. The length of each of the straight portion is 90 m and the ends are semi-circles. If the track is everywhere 14 m wide, find the area of the track. Also find the length of the outer running track.

Answer 1

Given, 

Inside perimeter of track = 400 m 

Length of straight portion = 90 m 

Width of path = 14 m 

Total length of straight path = 90 + 90 = 180 m 

Remaining length = 400 – 180 = 220 m 

This length includes two semi circles or a complete circle. 

So, 

2πr = 220 m 

= r = \(\frac{220\times7}{2\times22}\) = 35 m

Then, 

Area of path = (area of rectangles ABCD + rectangle EFGH + two semicircles) 

= 14 × 90 +14 × 90 + π [(25 + 14)² – 35²] 

[(a² – b²) = (a + b)(a - b)] 

= 2520 + \(\frac{22}7\times84\times14^2\)

Area of path = 6216 m² 

Length of outer track = 90 + 90 + 2πr 

r = 35 + 14 = 49 

= 180 + \(2\frac{22}7\times49^2\)

= 180 +308 = 488 m²