Triangle ABC is an equilateral triangle in which AB = (3x + 1)cm, BC = (2x + 3y +5)cm and AC = (x + 9y +6)cm. Find the values of x, y and the side of the equilateral triangle. Share with your friends Share 1 Varun.Rawat answered this We have,AB = 3x+1 cm; BC = 2x+3y+5 cm; CA = x+9y+6 cmSince, ABC is an equilateral ∆, thenAB = BC = CANow, AB = BC⇒3x + 1 = 2x + 3y + 5⇒x - 3y = 4 ....1Now, BC = CA⇒2x + 3y + 5 = x + 9y + 6⇒x - 6y = 1 ......2Subtracting 2 from 1, we get3y = 3 ⇒ y = 1Put y = 1 in 1, we getx - 3×1 = 4⇒x = 7Now, AB = 3x + 1 = 3×7 + 1 = 22 cmNow, BC = 2x+3y+5 = 2×7+3×1+5 = 14 + 3 + 5 = 22 cmNow, CA = x + 9 y + 6 = 7 + 9×1 + 6 = 22 cm 8 View Full Answer Prasad answered this AB = BC = AC AB = BC 3x + 1 = 2x + 3y + 5 3x - 2x - 3y = 5 - 1 x - 3 y = 4 → 1 BC = AC 2x + 3y + 5 = x + 9y + 6 2x + 3y - x - 9y = 6 - 5 x - 6y = 1 → 2 Subtracting 1 from 2 x - 6y - x + 3y = 1 - 4 = -3 -3y = -3 y = 1 Substituting y = 1 in 1 x = 7 Side = 22 cm 7
