Question

the inner perimeter of the race track is 400m and outer perimeter of the race track is 488m. the length of each straight portion is 90m find the cost of developing the track is rs 12.50 per metre square

Answer 1

Your question appears to be incomplete. As you didn't  mention about the shape of the race track. So, recheck your question and do get back to us.

Answer 2

Perimeter of the inner track = 2 straight lengths + 2 semicircles
                                    400 = 2(90) + 2($\pi$)(r)
                                    220 = 2($\pi$)(r)
                                    35m = r

Perimeter of the outer track = 2 straight lengths + 2 semicircles
                                    488 = 2(90) + 2($\pi$)(R)
                                    308 = 2($\pi$)(R)
                                    49m = R

The difference between the radii (49-35= 14m) is the width of the track,

Area of the track = 2(width of track)(lenght of straight portion) + 2($\pi$R$x^{2}$-$\pi$r$x^{2}$)
                           = 2(14)(90) + 2($\pi$)(49)$x^{2}$-$\pi$(35)$x^{2}$
                           = 2520 + 7390
                           = 9910 m$x^{2}$

Cost of developing the track = 12.5 * 9910 = Rs 123875