The length of EF is 9.
Using the diagram given for our Calculation;
- 2x + y + 2 = 3x + y (All sides of a rhombus are congruent) (1)
Also;
4x = y + 5 ___ (diagonals are perpendicular) (2)
From (2)
y = 4x - 5 ___(3)
Substituting (3) into (1)
2x + 4x - 5 + 2 = 3x + 4x - 5
6x - 3 = 7x - 5
6x - 7x = -5 + 3
-x = -2
x = 2
From (3)
y = 4(2) - 5
y = 3
The length of EF is :
2(2) + 3 + 2
4 + 3 + 2
= 9
The length of EF is 9.