Question
62
28
What is the relationship of the sides in this triangle based on the Pythagorean theorem?
m^2 + n^2= ___
28
What is the relationship of the sides in this triangle based on the Pythagorean theorem?
m^2 + n^2= ___
Answers
GPT-4o mini
To analyze the relationship of the sides in a triangle using the Pythagorean theorem, let's denote the lengths of the two legs of the triangle as \( m = 62 \) and \( n = 28 \). The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse \( c \) is equal to the sum of the squares of the lengths of the other two sides:
\[
c^2 = m^2 + n^2
\]
We can calculate \( m^2 + n^2 \):
\[
m^2 = 62^2 = 3844
\]
\[
n^2 = 28^2 = 784
\]
\[
m^2 + n^2 = 3844 + 784 = 4628
\]
So we have:
\[
m^2 + n^2 = 4628
\]
If we want to express this in the context of the Pythagorean theorem, it would be:
\[
c^2 = 4628
\]
Thus, if you are looking for the completed equation based on the Pythagorean theorem, it would be:
\[
m^2 + n^2 = 4628
\]
\[
c^2 = m^2 + n^2
\]
We can calculate \( m^2 + n^2 \):
\[
m^2 = 62^2 = 3844
\]
\[
n^2 = 28^2 = 784
\]
\[
m^2 + n^2 = 3844 + 784 = 4628
\]
So we have:
\[
m^2 + n^2 = 4628
\]
If we want to express this in the context of the Pythagorean theorem, it would be:
\[
c^2 = 4628
\]
Thus, if you are looking for the completed equation based on the Pythagorean theorem, it would be:
\[
m^2 + n^2 = 4628
\]