If the sum of the squares of the two shorter sides of a triangle is greater than the square of the longest side, the triangle is acute. However, if the sum of the squares of the two shorter sides of a triangle is smaller than the square of the longest side, the triangle is obtuse. If we take 11^2 + 17^2 we get 121 + 289 = 410.
Next we take our 4 answer choices and square those
21^2 = 441
20^2 = 400
19^2 = 361
18^2 = 324
441 is the only one larger than 410 so 21 must be the longest side to make that triangle obtuse.
