What Pythagorean triple is generated by multiplying each integer in the Pythagorean triple (20,21,29) by 5? explain
To find the Pythagorean triple generated by multiplying each integer in the given Pythagorean triple (20, 21, 29) by 5, we need to multiply each integer by 5.
Multiplying 20 by 5 gives us 100, multiplying 21 by 5 gives us 105, and multiplying 29 by 5 gives us 145. Therefore, the new Pythagorean triple is (100, 105, 145).
We can verify if this is a Pythagorean triple by using the Pythagorean theorem: a^2 + b^2 = c^2, where a, b, and c are the sides of a triangle.
For the original Pythagorean triple (20, 21, 29), we have:
20^2 + 21^2 = 400 + 441 = 841 = 29^2
And for the new Pythagorean triple (100, 105, 145), we have:
100^2 + 105^2 = 10000 + 11025 = 21025 = 145^2
Both equations satisfy the Pythagorean theorem, confirming that the new Pythagorean triple is indeed (100, 105, 145).