Verified Answer :

the answer is 17. you use pythagorean thereom

Here you want to use the Pythagorean Theorem.

\(a^{2} + b^{2} = c^{2}\) 

Remember that the hypotenuse ( c ) will always be the longest side, opposite of our right angle.

let's enter in the numbers on the picture into our theorem.

\(4^{2} + 1^{2} = c^{2}\)

now lets simplify

\(4^{2} = 16 \\ 1^{2} = 1 \\ \\ 16 + 1 = c^2 \\ \\ 17 = c^2 \\ \\ \sqrt{17} =c\)

and there you are! \(\sqrt{17} = c\)

Hope this helped!:)