Question

# The inside perimeter of a running track (shown) 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

## Solution:- The inside perimeter of the track = 400 m The total length of the two straight portions = 90 + 90 = 180 m Therefore the length of the remaining portion = 400 - 180 = 220 m Circumference of the two remaining semi-circular portions = πr + πr = 2πr 'r' is the radius. =>2πr=2×227×r=220 44r=220×7 r=35m So, the radius of the circular portion of the outer running running track = 35 m + 14 m = 49 m Area of the track = Area of the two rectangles of dimensions 90(\times\)14 + The area of the circular rings. =2×90×14+227×(492−352) =2520+227×(2401−1225) =2520+227×(2401−1225) =2520+22×11767 =6216 m2 Length of the outer running track = =2×90+2×227×49 = 180 + 308 Length of the outer running track = 488 m Answer MathematicsRD SharmaStandard X

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