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 Class 10 chapter 12
Page No. 236
Exercise 12.4
Question No. 8
Figure depicts a racing track whose left and right ends are semicircular.
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(i)The distance around the track along its inner edge
= AB + arcBEC + CD + arcDFA
= 106 + 1/2 × 2πr + 106 + 1/2 × 2πr
= 106 + 1/2 × 2 × 22/7 × 30 + 106 + 1/2 × 2 × 22/7 × 30
= 212 + 2 × 22/7 × 30 = 212 + 1320/7 = 2804/7
(ii) Area of Track = (Area of GHIJ – Area of ABCD) + (Area of semicircle HKI – Area of semicircle BRC) + (Area of semicircle GLJ – Area of semicircle AFD)
= (106 × 80 – 106 × 60) + 1/2 × 22/7 × [(40)² – (30)²] + 1/2 × 22/7 × [(40)² – (30)²]
= 106(80 – 60) + 1/2 × 22/7 × (700) + 1/2 × 22/7 × (700) = 2120 + 22/7 × (700) = 2120 + 2200 = 4320