Question

can you please help me solve this using the pythagorean theorem, and then tell me if it’s a pythagorean triple

Answer 1

Given a Right Triangle, you can use the Pythagorean Theorem to find the length "x", which states that:

$c^2=a^2+b^2$

Where "c" is the hypotenuse, and "a" and "b" are the legs of the Right Triangle.

In this case, you can set up that:

$\begin{gathered} c=26 \\ a=24 \\ b=x \end{gathered}$

Then, you can substitute values and solve for "x":

$\begin{gathered} 26^2=24^2+x^2 \\ \sqrt{26^2-24^2}=x \\ x=10 \end{gathered}$

By definition, you can identify if it is a Pythagorean Triple when "a", "b" and "c" are positive integers and this is true:

$c^2=a^2+b^2$

In this case, you know that they are positive integers and:

$\begin{gathered} 26^2=24^2+10^2 \\ 676=576+100 \\ 676=676 \end{gathered}$

Therefore, it is a Pythagorean Triple.

Hence, the answer is:

$x=10$

It is a Pythagorean Triple.