# 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 use the concept of perimeter or circles and areas of concentric circles.

We are given the following.

(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 semicircles HIJ and KLG = 60/2 = 30 m

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

JK = GH = 106 m

DJ = HB = 10 m

Diameter of semicircle HIJ = Diameter of semicircle KLG = 60 m

∴ Radius(r_{1}) = 60/2 = 30

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

= GH+ arc HIJ + JK + arc KLG

= 106 + 2πr_{1}/2 + 106 + 2πr_{1}/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

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

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

= (1060 + 1060 + π/2 × 700 + π/2 × 700) m^{2}

= (2120 + 700π) m^{2}

= (2120 + 700 × 22/7) m^{2}

= 2120 m^{2 }+ 2200 m^{2}

= 4320 m^{2}

**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:

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

The distance around the racing track along its inner edge and the area of the track are 2804/7 m and 4320 m^{2} respectively