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 + 1/2 x 22/7 x 492 – 1/2 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