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# The inner perimeter of a running track 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.

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If you open math book you will find a lot of mathematical questions but
youshould have solve this question.
It is from class 10 rd sharma chapter 15.4 mensuration .

In this question we have to find the area of the track and the length
of the outer running track given that inner perimeter of a running track
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.

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1. Let the radius of the inner semi-circle = r

And that of the outer semi-circle = R

Given,

Length of the straight portion = 90 m

Width of the track = 14 m

The inner perimeter of the track = 400 m

But,

Inner perimeter of the track = BF + FRG + GC + CQB = 400

90 + Ï€r + 90 + Ï€r = 400

2 Ï€r + 180 = 400

2 x 22/7 x r = 220

r = 35 m

So, the radius of the outer semi-circle = 35 + 14 = 49 m

Now,

Area of the track = 2[Area of the rectangle AEFB + Area of semi-circle APD â€“ Area of semi-circle BQC]

= 2[90 x 14 + Â½ x 22/7 x 492 â€“ Â½ x 22/7 x 352]

= 2[1260 + 11 x 7 x 49 â€“ 11 x 5 x 35]

= 2 [1260 + 3773 â€“ 1925]

= 3 x 3108

= 6216 m2

Thus,

The length of outer running track = AE + APD + DH + HSE

= 90 + Ï€R + 90 + Ï€R

= 180 + 2 Ï€R

= 180 + 2 x 22/7 x 49

= 180 + 308

= 488 m

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