ABCD is a rhombus. AB = 3x - 2, AC = 4x + 4, and BD = 2x. Find x.

Question: ABCD is a rhombus. AB = 3x - 2, AC = 4x + 4, and BD = 2x. Find x.Solution:A rhombus is a quadrilateral with four sides of equal length. Rhombuses have diagonals that bisect each other at right angles.Thus, we can consider the right triangle AED and use the Pythagorean Theorem to solve for x. From the problem:AD = 3x - 2BD = 2xAC = 4x + 4Because the diagonals bisect each other, we know:ED = xAE = 2x + 2Using the Pythagorean Theorem,a2 + b2 = c2∴ AE2 + ED2 = AD2⇒ (2x + 2)2 + (x)2 = (3x - 2)2⇒ 4x2 + 8x + 4 + x2 = 9x2 - 12x + 4⇒ 0 = 4x2 - 20xFactoring,0 = x and 0 = 4x - 20The first solution is nonsensical for this problem. 0 = 4x - 20∴ x = 5