What is the length of a diagonal of a rectangular picture whose side are 12 inches by 17 inches?

Use the Pythagorean Theorem for this problem:

$${{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{b}}}^{{\mathtt{2}}} = {{\mathtt{c}}}^{{\mathtt{2}}}$$

In other words: one side of the rectangle squared plus the other side squared equals the diagonal squared.

Therefore:

$${{\mathtt{12}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{17}}}^{{\mathtt{2}}} = {{\mathtt{c}}}^{{\mathtt{2}}}$$

$${\mathtt{144}}{\mathtt{\,\small\textbf+\,}}{\mathtt{289}} = {{\mathtt{c}}}^{{\mathtt{2}}}$$

$${\mathtt{433}} = {{\mathtt{c}}}^{{\mathtt{2}}}$$

Now take the square root of both sides:

c = $${\sqrt{{\mathtt{433}}}} = {\mathtt{20.808\: \!652\: \!046\: \!684\: \!811\: \!6}}$$