Mathematics to
5. The inside perimeter of a running track (shown in Fig. 20.24) is 400 . The length of
each of the straight portion is 90 m and the ends are semi-circles. If track 15
everywhere 14 m wide, find the area of the track. Also, find the length of the outer
running track.
Answers
Answer:
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Answer:
The inside perimeter of the track =400m
The total length of the two straight portions =90+90=180m
Therefore the length of the remaining portion =400−180=220m
Circumference of the two remaining semi-circular portions =πr+πr=2πr.
′
r ' is radius
-> 2πr=220
⇒ 2× 22/7
×r=220
∴ r=35m
So, the radius of the circular portion of the outer running running track =35m+14m=49m
Area of the track = Area of the two rectangles of dimensions + The area of the circular rings.
⇒ Area of track =2×90×14+ 22/7 ×[(49)² −(35)²]
⇒ Area of track =2520+ 22/7×(2401−1225)
⇒ Area of track =2520+ 22/7×1176
⇒ Area of track =2520+3696
∴ Area of track =6216m²
⇒ Length of the outer running track =2×90+2×22/7 ×49
⇒ Length of the outer running track =180+308
∴ Length of the outer running track =488m²
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