9514 1404 393
Answer:
b, c, a or AC, AB, BC
Step-by-step explanation:
The sum of the angle measures is 180°, so we have ...
∠A +∠B +∠C = 180°
(x^2 -18) +(2x^2 +3x) +(12x) = 180
3x^2 +15x = 198 . . . . add 18, simplify
x^2 +5x = 66 . . . . . . divide by 3
x^2 +5x -66 = 0 . . . subtract 66 to put in standard form
(x +11)(x -6) = 0 . . . . . factor
Solutions are x = -11, x = 6. Angle C requires x > 0, so the only useful solution is x = 6.
Then the angle measures are ...
∠A = x^2 -18 = 6^2 -18 = 18
∠B = 2x^2 +3x = x(2x +3) = 6(2·6 +3) = 90
∠C = 12x = 12·6 = 72
The angles, largest to smallest are B, C, A. Their opposite sides are in the same order, longest to shortest: b, c, a. Those sides will also be named AC, AB, BC.
