Pythagorean theorem. Game on.

$3^{2} + 4^{2} = 9 + 16 = 25$, so the hypotenuse is $\sqrt{25} = 5\textsf{.}$

$13^{2} - 5^{2} = 169 - 25 = 144$, so the other leg is $\sqrt{144} = 12\textsf{.}$

$5^{2} + 12^{2} = 25 + 144 = 169$, so the hypotenuse is $\sqrt{169} = 13\textsf{.}$

$25^{2} - 7^{2} = 625 - 49 = 576$, so the other leg is $\sqrt{576} = 24\textsf{.}$

$8^{2} + 15^{2} = 64 + 225 = 289$, so the hypotenuse is $\sqrt{289} = 17\textsf{.}$

$26^{2} - 10^{2} = 676 - 100 = 576$, so the missing leg is $\sqrt{576} = 24\textsf{.}$

$20^{2} + 21^{2} = 400 + 441 = 841$, so the hypotenuse is $\sqrt{841} = 29\textsf{.}$

$9^{2} + 12^{2} = 81 + 144 = 225$, so the hypotenuse is $\sqrt{225} = 15\textsf{.}$