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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 Answer

  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 + πr + 90 + πr = 400

    2 πr + 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 – Area of semi-circle BQC]

    = 2[90 x 14 + ½ x 22/7 x 492 – ½ x 22/7 x 352]

    = 2[1260 + 11 x 7 x 49 – 11 x 5 x 35]

    = 2 [1260 + 3773 – 1925]

    = 3 x 3108

    = 6216 m2

    Thus,

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

    = 90 + πR + 90 + πR

    = 180 + 2 πR

    = 180 + 2 x 22/7 x 49

    = 180 + 308

    = 488 m

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