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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×(492352)

=2520+227×(24011225)

=2520+227×(24011225)

=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


Mathematics
RD Sharma
Standard X

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