Posted by Nashea on Friday, October 2, 2009 at 10:50am.
1, 2, 3,and 5 are right i think but i don't know about 4.
#4 is also correct since
8^2 + 10^2 is not equal to 12^2
I would prefer that you call them Pythagorean triples.
1. yes
2. yes
3. 500 kg is OK. Jersey cows weigh less; black angus weigh more.
4. correct. A correct "perfect triple" would be 6,8,10. a^2 + b^2 = c^2 must be obeyed.
5. yes
#1. 3 gal and 2 qt subtracted from 8 gal and 7 qt= 6 gal and 1 qt?
There is a problem with the question, 1 gallon equals 4 qts, so 8 gal and 7 qts is not normal. Was there a typo? Was it 8 gal and 7 pts? (1 gal = 8 pts)
8 gal- 7 qts - 3 gal 2qts
= 9 gal 3 qts - 3 gal 2qts
= 6 gal 1 qt.
8 gal - 7 pts - 3 gal 2 qts
=8 gal - 7 pts - 3 gal 4 pts
= 5 gal 3 pts.
#2,3 and 5 are correct.
For #4 it is not clear to me what a perfect triple is supposed to mean.
If you have done Pythagoras theorem, it could be asking if the three numbers form the sides of a Pythagorean triangle (answer=no).
It could also mean if the numbers can represent the sides of a triangle, which requires that 8+10>12, 8+12>10 and 10+12>8. The answer is yes in this case.
Then again, it could be asking if the average (mean) of the three numbers equals the middle number. The answer is yes here.
We can go on and on. Perhaps you can tell us what your teacher means by a perfect triple.
in the eample they use 3,4, and 5
so 3 to the power of 2=9
4 to the power of 2 =16
5 to the power of 2=25
9+16=25
a perfect triple
this was also there
All the triples that you have seen, and many more, were known by the Babylonians
more than 4,000 years ago. Stone tablets that had dozens of perfect triples carved into them
have been found. The basis of the Pythagorean theorem was understood long before the
time of Pythagoras (ca. 540 B.C.). The Babylonians not only understood perfect triples but
also knew how triples related to a right triangle.
So this confirms that question 1 refers to Pythagorean triples. As everybody has suggested, the answer is no because
8²+10²=164
12²=144
So the triple is not a Pythagorean triple.
I cannot agree more with Reiny:
"I would prefer that you call them Pythagorean triples. "
round 44-21