Question

At 3 O’ clock, the tip of the hour hand was 17 cm from the tip of the minute hand. At 6 O’ clock, this distance becomes 23 cm. What is the distance (in cm) between their tips at 12 O’ clock?



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Answer 1

Given : At 3 O’ clock, the tip of the hour hand was 17 cm from the tip of the minute hand. At 6 O’ clock, this distance becomes 23 cm.

To Find : What is the distance (in cm) between their tips at 12 O’ clock?

Solution:

Let say  Hour Hand Length = H

& Minute Hand Length = M

At 3 O’ clock, the tip of the hour hand was 17 cm from the tip of the minute hand

At 3 O’ clock angle between Hands  = 90°

=> M² + H² = 17²

At 6 O’ clock, this distance becomes 23 cm.  

At 6 O’ clock angle between Hands  = 180°  ( opposite direction)

M + H  = 23

M = 23 - H

(23 - H)² + H² = 17²

=> 23² + H² - 46H + H² = 17²

=> 2H² - 46H + 529 = 289

=> 2H² - 46H + 240 =0

=> H² - 23H +  120 = 0

=> H² - 15H - 8H  + 120 = 0

=> (H - 15)(H - 8) = 0

=> H = 15  , 8

=> M = 8 , 15

Generally Minute hand is longer than Hour Hand

Hence

Minute Hand = 15 cm

Hour Hand =  8 cm

at 12 O’ clock angle between hands = 0°

Hence  distance (in cm) between their tips = 15 - 8

=7 cm

distance (in cm) between their tips at 12 O’ clock = 7 cm

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Answer 2

Step-by-step explanation:

hope it's help full for u