At 6 o'clock, the tip of the hour hand was 23cm from the tip of the minute hand. At 9 o'clock, this distance was only 17cm. By how many centimeters does the minute hand's length exceed the hour hand's length? ( no diagram provided) I tried to use Pythagorean and in the end, I didn't know what to do after I went from there.

SydSu22 Apr 30, 2019

#1**+1 **

*At 6 o'clock, the tip of the hour hand was 23cm from the tip of the minute hand. At 9 o'clock, this distance was only 17cm. By how many centimeters does the minute hand's length exceed the hour hand's length? ( no diagram provided) I tried to use Pythagorean and in the end, I didn't know what to do after I went from there. *

You were on the right track with Pythagorean. At six o'clock, the hands are in a straight line so we know the total length of the two hands is 23 cm. One hand length we will call L so the other hand is (23 – L).

Draw your triangle when the hour hand is at nine and the minute hand at twelve. One hand length is L, the other hand length is (23 – L), and the hypotenuse is 17.

so, by the Pythagorean Theorem, L^{2} + (23 – L)^{2} = 17^{2}

multiply it on out L^{2} + (529 – 46L + L^{2}) = 289

remove parentheses and rearrange terms 2L^{2} – 46L + 240 = 0 (240 came from 529 minus 289)

this will factor to (2L – 16)(L – 15) = 0

set each term to zero 2L – 16 = 0 thus L = 8

L – 15 = 0 thus L = 15

the minute hand is longer, so it's the one that's 15 and the hour hand is 8

so the minute hand length exceeds the hour hand length by 15 – 8 = **7 cm**

17 cm

Guest May 1, 2019

#1**+1 **

Best Answer

*At 6 o'clock, the tip of the hour hand was 23cm from the tip of the minute hand. At 9 o'clock, this distance was only 17cm. By how many centimeters does the minute hand's length exceed the hour hand's length? ( no diagram provided) I tried to use Pythagorean and in the end, I didn't know what to do after I went from there. *

You were on the right track with Pythagorean. At six o'clock, the hands are in a straight line so we know the total length of the two hands is 23 cm. One hand length we will call L so the other hand is (23 – L).

Draw your triangle when the hour hand is at nine and the minute hand at twelve. One hand length is L, the other hand length is (23 – L), and the hypotenuse is 17.

so, by the Pythagorean Theorem, L^{2} + (23 – L)^{2} = 17^{2}

multiply it on out L^{2} + (529 – 46L + L^{2}) = 289

remove parentheses and rearrange terms 2L^{2} – 46L + 240 = 0 (240 came from 529 minus 289)

this will factor to (2L – 16)(L – 15) = 0

set each term to zero 2L – 16 = 0 thus L = 8

L – 15 = 0 thus L = 15

the minute hand is longer, so it's the one that's 15 and the hour hand is 8

so the minute hand length exceeds the hour hand length by 15 – 8 = **7 cm**

17 cm

Guest May 1, 2019