  Question

The inside perimeter of a running track (shown in the following figure) 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. Solution

It is given that, and  We know that the circumference C of semicircle of radius be r is $C=\mathrm{\pi }r$ The inside perimeter of running track is the sum of twice the length of straight portion and circumferences of semicircles. So, inside perimeter of running track = 400 m Thus, radius of inner semicircle is 35 m. Now, radius of outer semi circle r' = 35 + 14 = 49 m Area of running track =             $=2×90×14+2×\frac{\mathrm{\pi }\left(49{\right)}^{2}}{2}-2×\frac{\mathrm{\pi }\left(35{\right)}^{2}}{2}$             $=2520+\mathrm{\pi }×\left(49+35\right)\left(49-35\right)$             $=2520+\frac{22}{7}×84×14$             Hence, the area of running track = 6216 m2 Now, length L of outer running track is L = 2 × l + 2$\mathrm{\pi }$r'    $=2×90+2\mathrm{\pi }×49$    $=180+2×\frac{22}{7}×49$        Hence, the length L of outer running track is 488 m.   MathematicsRD Sharma (2020, 2021)All

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