Answer
There are 2 outcomes in the event P.
\[P=\{(3,\text{ }4,\text{ }5),\text{ }(4,\text{ }3,\text{ }5)\}\]
Work Step by Step
The Pythagorean Theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Suppose the height, length and hypotenuse of a right triangle are a, b and c, respectively.
The Pythagorean theorem states that every right triangle has side lengths satisfying the formula ${{a}^{2}}+{{b}^{2}}={{c}^{2}}$.
Let $c=5$; then ${{a}^{2}}+{{b}^{2}}={{5}^{2}}=25$.
Hence, the possible values of a and b satisfying the above equation are 3 and 4 or 4 and 3.
The possible outcomes of the event P are:
\[\begin{align}
& P=\left\{ (a,\text{ }b,\text{ }c):{{a}^{2}}+{{b}^{2}}=25 \right\} \\
& P=\{(3,\text{ }4,\text{ }5),\text{ }(4,\text{ }3,\text{ }5)\} \\
\end{align}\]
