To determine if the sets of numbers (6, 8, 10) and (t, 12, 13) are Pythagorean triples, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
For the set (6, 8, 10):
Let's consider the sides 6 and 8 as the legs of the right triangle and 10 as the hypotenuse. According to the Pythagorean theorem:
6^2 + 8^2 = 10^2
36 + 64 = 100
100 = 100
Since the equation is true, the set (6, 8, 10) is a Pythagorean triple.
For the set (t, 12, 13):
Let's consider the sides t and 12 as the legs of the right triangle and 13 as the hypotenuse. According to the Pythagorean theorem:
t^2 + 12^2 = 13^2
t^2 + 144 = 169
t^2 = 169 - 144
t^2 = 25
t = ±5
Since t = ±5 satisfies the equation, the set (t, 12, 13) can be a Pythagorean triple.
In conclusion, the set (6, 8, 10) is a Pythagorean triple because it satisfies the Pythagorean theorem. The set (t, 12, 13) can also be a Pythagorean triple for values of t = ±5, as it satisfies the Pythagorean theorem as well.
The sets of numbers are 6,8,10 and t,12,13 are Pythagorean triples. Use what you know about the Pythagoream theorem snd explain or show why they are Pythagorean triples
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