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15 Jul 2012, 19:30
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I want to understand right triangles a little better.
So if you have a Triangle and the given facts are:
1) Right triangle (so one side is 90*)
2) The hypotunse is equal to 10
Can we conclude the triangle is a 6-8-10 ( a variant of the 3-4-5) triangle? If not, can we calculate the permiter of the triangle?
How about the introduction of a new fact:
1) Right triangle (so one side is 90*)
2) The hypotunse is equal to 10
3) All the sides of the triangle are integer values.
Now can we concludes it is a 6-8-10 triangle?
With the exception of having a 90* degree angle, what conditions do we need to ensure a triangle is a Pythagorean triangle?
So if you have a Triangle and the given facts are:
1) Right triangle (so one side is 90*)
2) The hypotunse is equal to 10
Can we conclude the triangle is a 6-8-10 ( a variant of the 3-4-5) triangle? If not, can we calculate the permiter of the triangle?
How about the introduction of a new fact:
1) Right triangle (so one side is 90*)
2) The hypotunse is equal to 10
3) All the sides of the triangle are integer values.
Now can we concludes it is a 6-8-10 triangle?
With the exception of having a 90* degree angle, what conditions do we need to ensure a triangle is a Pythagorean triangle?
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15 Jul 2012, 23:24
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alphabeta1234
There are various ways in which you can have a right triangle with hypotenuse 10.
The sides could be 1, \(\sqrt{99}\), 10
or \(\sqrt{2}\), \(\sqrt{98}\), 10
or 6, 8, 10
etc
If sides are integral, it does add constraint to the values that the sides can take. Pythagorean triplets give sides of right triangles that have all integral sides. But that doesn't ensure that the hypotenuse will imply a single value for the other two sides in all cases (but it does in most).
If hypotenuse is 10, the sides will be 6 and 8 but if the hypotenuse is 65, the other two sides could be (16, 63) or (33, 56)
Check out more here: https://en.wikipedia.org/wiki/Pythagorean_triple
16 Jul 2012, 16:45
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Hey Karishma,
What about
How about the introduction of a new fact:
1) Right triangle (so one side is 90*)
2) The hypotunse is equal to 10
3) All the sides of the triangle are integer values.
Does the third condition gaurentee that we have a unique triplet triangle? Because as you mentioned we can have a right triangle with hypotunse of 10 with three possible side orders:
1) 1, \(\sqrt{99}\), 10
2) \(\sqrt{2}\), \(\sqrt{98}\), 10
3) 6,8,10
But notice only one of choices has all of its sides as integer values!! (1) and (2) do not have integer values as sides.
Can I therefore state the condition :
IF the triangle is:
1) A right triangle
2) One of the sides is triplet value (3,4,5) (6,8,10) (5,12,13) (8,15,17) etc
3) All of the sides are integer value
Then the triangle is a triplet and unique?
What about
How about the introduction of a new fact:
1) Right triangle (so one side is 90*)
2) The hypotunse is equal to 10
3) All the sides of the triangle are integer values.
Does the third condition gaurentee that we have a unique triplet triangle? Because as you mentioned we can have a right triangle with hypotunse of 10 with three possible side orders:
1) 1, \(\sqrt{99}\), 10
2) \(\sqrt{2}\), \(\sqrt{98}\), 10
3) 6,8,10
But notice only one of choices has all of its sides as integer values!! (1) and (2) do not have integer values as sides.
Can I therefore state the condition :
IF the triangle is:
1) A right triangle
2) One of the sides is triplet value (3,4,5) (6,8,10) (5,12,13) (8,15,17) etc
3) All of the sides are integer value
Then the triangle is a triplet and unique?
