For this left triangle what is the length of side c?

To answer this question you need to remember the Pythagorean theorem which relates the lengths of the sides of a right triangle to each other via the formula \( a^2 + b^2 = c^2 \)where a and b are the height and width of the triangle and c is the hypotenuse.

We're looking for c so the equation becomes: \( c^2 = a^2 + b^2\)
\(c = \sqrt{a^2 + b^2}\)
Substituting our variables:
\( c = \sqrt{3^2 + 3^2}\)
\(c = \sqrt{9 + 9}\)
\(c = \sqrt{18}\)
Simplifying, \( \sqrt {18} = \sqrt {9 \times 2} = \sqrt 9 \sqrt 2 = 3\sqrt 2\)