Question

In the figure (ii) given below, the inside perimeter of a practice running track
with semi-circular ends and straight parallel sides is 312 m. The length of the
straight portion of the track is 90 m. If the track has a uniform width of 2 m
throughout, find its area.
​

Answer 1

Answer:

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Step-by-step explanation:

The length of the straight portion of the track is 90 m.and

The inside perimeter 312m

∴πr+length+πr+length=312

⇒πr+90+πr+90=312

⇒2πr=312−180

⇒2πr=132

⇒r=

2π

132

⇒r=

2×22

132×7

⇒r=

44

924

⇒r=21

Width of the running track =2m

∴ Radius of outer perimeter=21+2=23

∴ Area of outer perimeter =

2

π(23)

2

+(90×23×2)+

2

π(23)

2

=

7×2

22(23)

2

+(90×23×2)+

7×2

22(23)

2

=831.285+4140+831.285=5802.57

∴ Area of inner perimeter =

2

π(21)

2

+(90×21×2)+

2

π(21)

2

=

7×2

22(21)

2

+(90×21×2)+

7×2

22(21)

2

=693+3780+693=5166

Area of the track= Area of outer perimeter − Area of inner perimeter

=5802.57−5166 =636.57m

2