What is the length of a diagonal brace that could be used for a wall 9 feet high and 12 feet long

You use the pythagorean theorem to solve this problem. The theorem is a^2+b^2=c^2, where c^2 is the length of the hypotenuse of the triangle, or the side that's the longest and is opposite the right angle of the right triangle. Note that this theorem is applicable because a wall has right angles and it is assumed that the diagonal brace would form a right triangle (the diagonal brace is the hypotenuse). Next, you substitute the values of 9 and 12 for a and b, and then you proceed to solve this algebraically to get c after taking the square roots of both sides of the equation to get c from c^2.