Question

the inside perimeter of a running track is 400 meter lenth of each of straight portion is 90 meter and the ends are sami circle if track is everywhere 14 meter wide find the area of track also the length of outer running track

Answer 1

consider the attached figure,

$inner edge= \pi r + l + \pi r + l = 2 \pi r+2l = 2 \pi r + 2*90 = 400$
⇒r=35m
$outer edge= \pi (r+14) + l + \pi (r+14) + l = 2\pi (35+14) + 2*90$
=488m
$area= \pi (49^{2} - 35^{2} )/2+90*14+\pi (49^{2} - 35^{2} )/2+90*14$
=6216 m²