Answer:
x = 9, y = 12, z = 11
Explanation:
A rhombus is a quadrilateral (has four sides and four angles) with four equal sides. Opposite sides of a rhombus are parallel to each other and the diagonals bisect each other at right angles i.e. 90°.
Given the rhombus ABCD:
(6x + 4) = (4y + 10) = (8x − 14) = (7y − 26) [the sides of a rhombus are equal].
Hence; 6x + 4 = 8x - 14
8x - 6x = 14 + 4
2x = 18
x = 9
Therefore the side length = 6x + 4 = 6(9) + 4 = 58 inches
Also: 4y + 10 = 7y - 26
7y - 4y = 10 + 26
3y = 36
y = 12
(8z + 2) = 90° (diagonals of a rhombus bisect each other)
8z + 2 = 90
8z = 90 - 2
8z = 88
z = 11