Missing side from area or perimeter (SAT/PSAT 8/9/10). Game on.

Perimeter $P = 2\ell + 2w$, so $40 = 2(8) + 2w$. Then $40 = 16 + 2w$, so $2w = 24$ and $w = 12\text{ cm}\textsf{.}$

Perimeter $P = 2\ell + 2w$, so $50 = 2(10) + 2w$. Then $50 = 20 + 2w$, so $2w = 30$ and $w = 15\text{ m}\textsf{.}$

Area $A = \ell w$, so $72 = 9w$. Dividing gives $w = 8\text{ in}\textsf{.}$

A square has $4$ equal sides, so $P = 4s$. Then $s = \dfrac{36}{4} = 9\text{ cm}\textsf{.}$

A square has $4$ equal sides, so $P = 4s$. Then $s = \dfrac{64}{4} = 16\text{ m}\textsf{.}$

Perimeter $P = 2\ell + 2w$, so $30 = 2\ell + 2(5)$. Then $30 = 2\ell + 10$, so $2\ell = 20$ and $\ell = 10\text{ m}\textsf{.}$

Area $A = \ell w$, so $56 = 8w$. Dividing gives $w = 7\text{ cm}\textsf{.}$

A square has $4$ equal sides, so $P = 4s$. Then $s = \dfrac{100}{4} = 25\text{ in}\textsf{.}$