Use the pythagorean Theorem to determine which sets of numbers is a Pythagorean Triple:
11, 60, 62
20, 21, 29
9, 12, 14
To determine if a set of numbers is a Pythagorean Triple, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's start with the first set: 11, 60, 62
a = 11, b = 60, c = 62
a^2 + b^2 = c^2
11^2 + 60^2 = 121 + 3600 = 3721
c^2 = 62^2 = 3844
Since 3721 is not equal to 3844, the first set 11, 60, 62 is NOT a Pythagorean Triple.
Moving on to the second set: 20, 21, 29
a = 20, b = 21, c = 29
a^2 + b^2 = c^2
20^2 + 21^2 = 400 + 441 = 841
c^2 = 29^2 = 841
Since 841 is equal to 841, the second set 20, 21, 29 IS a Pythagorean Triple.
Lastly, let's check the third set: 9, 12, 15
a = 9, b = 12, c = 15
a^2 + b^2 = c^2
9^2 + 12^2 = 81 + 144 = 225
c^2 = 15^2 = 225
Since 225 is equal to 225, the third set 9, 12, 15 IS a Pythagorean Triple.
So, the Pythagorean Triples from the given sets of numbers are:
- 20, 21, 29
- 9, 12, 15
the third set is
9, 12, 14
not 15.
Let's recheck the third set: 9, 12, 14
a = 9, b = 12, c = 14
a^2 + b^2 = c^2
9^2 + 12^2 = 81 + 144 = 225
c^2 = 14^2 = 196
Since 225 is NOT equal to 196, the third set 9, 12, 14 is NOT a Pythagorean Triple.
So, the correct Pythagorean Triples from the given sets of numbers are:
- 20, 21, 29