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Answers
QUESTION:
To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in Fig. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?
ANSWER:
- Distance between both the flags = √61 m.
- Rashmi has to post a blue flag in the fifth line at a distance of 22.5 m.
GIVEN:
- 100 flower pots have been placed at a distance of 1 m from each other along AD.
- Niharika runs 1/4 th the distance AD on the second line and posts a green flag.
- Preet runs 1/5 th the distance AD on the eighth line and posts a red flag.
- Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags
TO FIND:
- Distance between both the flags.
- Where should Rashmi post her flag.
EXPLANATION:
As 100 flower pots are place along AD.
Length of AD = 100 m
Distance covered by Niharika = 1/4 × 100
Distance covered by Niharika = 25 m
Distance covered by Preet = 1/5 × 100
Distance covered by Preet = 20 m
Let AP be the distance covered by Niharika.
AP = 25 m
Let BC be the distance covered by Preet.
BC = 20 m
AP = AE + PE
AE = BC = 20 m
25 = 20 + PE
PE = 5 m.
Let distance between 8th and 2nd line be AB.
Distance between 8th and 2nd line = 8 - 2 [ Lines have been drawn at a distance one meter each ]
AB = 6 m.
Let PC be the distance between both the flags.
By Pythagoras Theorem.
PC² = EC² + PE²
PE = 5 m
EC = AB = 6 m
PC² = 5² + 6²
PC² = 25 + 36
PC = √61
Hence distance between both the flags = √61 m.
Distance between 8th and 2nd line = 6 m
Midpoint = 6/2 = 3 m
Rashmi has to post the flag in the 5th line. [ As 2 + 3 = 5 (or) 8 - 3 = 5 ]
Rashmi post the flag at the midpoint of the line segment which is √61 m.
Midpoint = √61 / 2
Let M be the midpoint of 2nd and 8th line
AM = 3 m
AP = 25 m
Let N be the midpoint of the line segment.
PN = √61 / 2
AM = GN = 3 m
By Pythagoras Theorem.
PN² = GN² + PG²
(√61 / 2)² = 3² + PG²
61/4 - 9 = PG²
(61 - 36)/4 = PG²
PG² = 25/4
PG = 5/2
PG = 2.5
AP = AG + PG
25 = AG + 2.5
AG = 22.5 m
AG = MN = 22.5 m
Hence Rashmi has to post a blue flag in the fifth line at a distance of 22.5 m.
NOTE : REFER ATTACHMENT FOR DIAGRAM.
