Page 167 - Ganit Kaushal

(ii) Mark ‘B’ at the point where Akshi will be after she has run 500 m.

(iii) Now, Akshi ran 1000 m. How many full rounds has she finished running around her track?
Mark her position as ‘C’.
(iv) Mark ‘X’ at the point where Toshi will be after she has run 250 m.
(v) Mark ‘Y’ at the point where Toshi will be after she has run 500 m.
(vi) Now, Toshi ran 1000 m. How many full rounds has she finished running around her track?
Mark her position as ‘Z’. (NCERT)

Sol. (a) Each track is a rectangle. Akshi’s track has a length of 70 m and a breadth of 40 m. So, the distance
covered by Akshi in one complete round = 2 × (70 + 40) m = 220 m.
Therefore, the total distance covered by Akshi in 5 rounds = 5 × 220 m = 1100 m.
(b) Toshi’s track has a length of 60 m and a breadth of 30 m. So, the distance covered by Toshi in one
round = 2 × (60 + 30) m = 180 m. Therefore, the total distance covered by Toshi in 7 rounds =
7 × 180 m = 1260 m. So, we conclude that Toshi ran a longer distance than Akshi.
(c) (i) The distance between any two black dots is 10 m, as shown by the red arrow in the figure.
For Akshi to run 250 m, she has C 70 m
to complete 1 full round of 220 m Z 60 m Y
plus 30 m more. So, she must be at

the third dot after her starting point. 40 m
So mark ‘A’ at the third dot after her 30 m
starting point as shown in the figure. X
(ii) ‘B’ is marked in the figure by using the
same logic as above. 10 m
(iii) Akshi ran: 4 × 220 + 120 = 880 + 120 A
= 1000 m. So, she completes 4 full B Starting Point Starting Point
rounds; still she needs to run 120 m. for Toshi for Akshi
So, ‘C’ should be marked after 12 black dots from her starting point as shown in the figure.

(iv) Marked ‘X’ at the point where Toshi will be after running 250 m, using the same logic as in
part (i).

(v) Marked ‘Y’ at the point where Toshi will be after running 500 m, using the same logic as in
part (ii).
(vi) Toshi ran: 5 × 180 + 100 = 900 + 100 = 1000 m. So, Toshi completes 5 full rounds; still she
needs to run 100 m. So, ‘Z’ should be marked after 10 dots from her starting point as shown
in the figure.
Ex 4. In races, usually there is a common finish line for all the runners. Here are two 150 m
square running tracks with the inner track of 100 m on each side and the outer 100 m
track of 150 m on each side. The common finishing line for both runners is
shown by the flags in the figure, which are at the centre of one of the sides of
the tracks. If the total race is of 350 m, then we have to find out where the
starting positions of the two runners should be on these two tracks so that they
both have a common finishing line after they run for 350 m. Mark the starting
points of the runner on the inner track as ‘A’ and the runner on the outer track
as ‘B’. (NCERT) Common Finishing Line

Perimeter and Area 165