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Two sides of the square, along with the diagonal, form a right triangle. Therefore, we apply the Pythagorean theorem: a2 + b2 = c2.
a and b are the sides of the triangle that connect with the right (ninety-degree) angle, and c is the side opposite the right angle.
122 + 122 = c2
144 + 144 = c2
288 = c2
288 = c2 Take the square root of both sides of the equation.
288 = c
The square root of 288 is approximately 16.97. Therefore, the diagonal measure of a twelve foot square is approximately 16.97.
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