It is important to know that a Pythagorean Triple is a set of three numbers that satisfy the Pythagorean Theorem
[tex]c^2=a^2+b^2[/tex]
Then, we form the following equations
[tex]\begin{gathered} a=x^2-y^2 \\ b=2xy \\ c=x^2+y^2 \end{gathered}[/tex]
These equations are deducted from the Pythagorean Theorem. The correct numbers must satisfy these equations for a = 7, b = 24, and c = 25.
Now, we just evaluate each answer choice to see which one meets these equations.
Option A is not correct because x must be greater than y, otherwise, the solution won't be real.
Option B.
[tex]a=3^2-2^2=9-4=5[/tex]
Option B is not correct because doesn't meet the first expression.
Option D.
[tex]\begin{gathered} a=4^2-3^2=16-9=7 \\ b=2\cdot4\cdot3=24 \\ c=4^2+3^2=16+9=25 \end{gathered}[/tex]
Hence, D is the correct answer.
