MAST Grade 8 Pythagorean Theorem. Practice it free.

Both points have $x = 5$, so the length is $|9 - (-3)| = 12$.

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

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

The string is the hypotenuse: $25^{2} - 7^{2} = 625 - 49 = 576$, so the height is $\sqrt{576} = 24$ meters.

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

$\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$.

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

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