Fig. 12.26 depicts a racing track whose left and right ends are semicircular. The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find :
(i) the distance around the track along its inner edge
(ii) the area of the track.

Solution:

We are given the following information:

(i) A racing track whose right and left ends are semicircular.

(ii) The distance between the 2 inner parallel line segments is 60 m and they are 106 m long.

(iii) Width of track = 10 m

Radii of the inner semicircles HIJ and KLG (r₁) = 60/2 = 30 m

Radii of the outer semicircles BCD and EFA = 30 m + 10 m = 40 m

JK = GH = 106 m

DJ = HB = 10 m

(i) The distance around the track along its inner edge.

= GH + arc HIJ + JK + arc KLG

= 106 + 2πr₁/2 + 106 + 2πr₁/2

= 106 + π × 30 + 106 + π × 30

= 212 + 1320/7

= (1484 + 1320)/7

= 2804/7 m

(ii) Radius of semicircle BCD = Radius of semicircle EFA

(r₂) = 30 m + 10 = 40 m

Area of the track = Area of rectangle ABHG + Area of rectange KJDE + (Area of semicircle BCD - Area of semicircle HIJ) + (Area of semicircle EFA - Area of semicircle KLG)

= {(106 × 10) + (106 × 10) + [1/2π (40)² - 1/2π (30)²] + [1/2π (40)² - 1/2π (30)²]}

= {1060 + 1060 + [1/2π (1600 - 900)] + [1/2π (1600 - 900)] }

= 1060 + 1060 + π/2 × 700 + π/2 × 700

= 2120 + 700π)

= 2120 + 700 × 22/7

= 2120 + 2200 

= 4320 m²

☛ Check: NCERT Solutions Class 10 Maths Chapter 12

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Video Solution:

Fig. 12.26 depicts a racing track whose left and right ends are semicircular. The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find : (i) the distance around the track along its inner edge (ii) the area of the track.

NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.3 Question 8

Summary:

The given figure depicts a racing track whose left and right ends are semicircular. The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, (i) the distance around the track along its inner edge is 2804/7 m and (ii) the area of the track is 4320 m².

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☛ Related Questions:

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