This is a word problem, geometry

Question

The sides of a triangle are x, x - 4, 33, where the length of the longest side is the integer given. What value(s) of x make it an obtuse triangle? Answer is simplest radical form.

Answer 1

The three sides of a triangle should be proportional as either an acute, obtuse, or right triangle. This relationship is found by using a² + b² = c². Since the problem says this is an obtuse triangle, a² + b² < c², since one side is longer than the others. So you need to create an equation that relates x² + (x-4)² < 33² and solve it that way. This gives you 2x²-8x+16 < 1089, which then becomes 2x²-8x-1073 < 0, which you need to use the quadratic formula to solve. In simplest radical form the answer is: x = 2 +/- 1/2 * (square root (2162)). Hope it helps!!

Answer 2

Use Pythagoras

33³ > x² + (x - 4)²

Can you solve for x and answer?