8.G.B.7 math practice. Learn by doing.

The legs are $12$ and $35$. By the Pythagorean theorem, $12^{2} + 35^{2} = 144 + 1{,}225 = 1{,}369$, so the hypotenuse is $\sqrt{1{,}369} = 37$.

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

The walk forms the legs of a right triangle: $\sqrt{8^{2} + 15^{2}} = \sqrt{64 + 225} = \sqrt{289} = 17$ blocks.

Area $A = \ell w$, so $120 = 8w$ and $w = 15$. The diagonal is the hypotenuse of a right triangle with legs $8$ and $15$: $\sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17\text{ cm}\textsf{.}$

The legs are $16$ and $30$. By the Pythagorean theorem, $16^{2} + 30^{2} = 256 + 900 = 1{,}156$, so the hypotenuse is $\sqrt{1{,}156} = 34$.

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

The wire is the hypotenuse: $26^{2} - 24^{2} = 676 - 576 = 100$, so the pole is $\sqrt{100} = 10$ meters tall.

Let the missing leg be $x$. Then $x^{2} + 18^{2} = 30^{2}$, so $x^{2} = 30^{2} - 18^{2} = 900 - 324 = 576$ and $x = \sqrt{576} = 24$.