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.
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