Question

Rhombus ABCD has side lengths of (6x + 4) inches, (4y + 10) inches, (8x − 14) inches, and (7y − 26) inches. The diagonals are 80 inches and 84 inches and intersect forming an angle of (8z + 2)°.

Answer 1

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