Question

select the correct answer.
rhombus efgh is shown. what is the length of \\(\overline{ef}\\)?
(the figure of rhombus efgh with labeled sides and diagonals: ef is labeled 2x + y + 2, hg is labeled 3x + y, ehs diagonal segment ej? no, the diagonal segments: one diagonal has segments 4x (from h to j) and y + 5 (from j to f); the other diagonal is from e to g, not labeled with expressions here. options: a. 3, b. 6, c. 8, d. 9)

Explanation:

Step1: Set sides equal (rhombus property)

$2x + y + 2 = 3x + y$

Step2: Solve for x

$2x + 2 = 3x \implies x = 2$

Step3: Set diagonals halves equal

$4x = y + 5$

Step4: Substitute x=2, solve for y

$4(2) = y + 5 \implies 8 = y + 5 \implies y = 3$

Step5: Calculate length of $\overline{EF}$

Substitute $x=2, y=3$ into $2x + y + 2$:
$2(2) + 3 + 2 = 4 + 3 + 2$

Answer:

D. 9