2. Use the pythagorean Theorem to determine which sets of numbers is a Pythagorean Triple:
a. 11, 60, 62
b. 20, 21, 29
c. 9, 12, 14
a. To determine if 11, 60, 62 is a Pythagorean Triple, we can use the Pythagorean Theorem:
a^2 + b^2 = c^2
where a and b are the two shorter sides of the triangle, and c is the hypotenuse. Plugging in the values we have:
11^2 + 60^2 = 62^2
121 + 3600 = 3844
3721 = 3844
Since 3721 does not equal 3844, this set of numbers is not a Pythagorean Triple.
b. To determine if 20, 21, 29 is a Pythagorean Triple, we can use the Pythagorean Theorem:
20^2 + 21^2 = 29^2
400 + 441 = 841
Since 841 equals 841, this set of numbers is a Pythagorean Triple.
c. To determine if 9, 12, 14 is a Pythagorean Triple, we can use the Pythagorean Theorem:
9^2 + 12^2 = 14^2
81 + 144 = 196
Since 225 does not equal 196, this set of numbers is not a Pythagorean Triple.