The problem asks whether the equation $n^2 = m^2 + o^2$ holds for the given right triangle with sides $n$, $m$, and $o$. We need to determine if the given equation is consistent with the Pythagorean theorem.

1. Problem Description

The problem asks whether the equation $n^2 = m^2 + o^2$ holds for the given right triangle with sides $n$, $m$, and $o$. We need to determine if the given equation is consistent with the Pythagorean theorem.

2. Solution Steps

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).

Looking at the diagram, we can see that $m$ is the hypotenuse, and $n$ and $o$ are the legs. Therefore, according to the Pythagorean theorem, the correct equation should be:

$m^2 = n^2 + o^2$

The given equation is $n^2 = m^2 + o^2$.

This can be rearranged as $n^2 - m^2 = o^2$, or $0 = m^2 - n^2 + o^2$.

Since $m$ is the hypotenuse, $m$ must be the longest side, so $m^2 > n^2$, which makes $m^2 - n^2$ positive. If $o^2$ is also positive, then the given expression cannot be equal to

0.

Comparing $m^2 = n^2 + o^2$ with the provided $n^2 = m^2 + o^2$, we see that they are different. The correct equation must have $m$ (the hypotenuse) isolated on one side.

3. Final Answer

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