Answer:
18 units
Step-by-step explanation:
Let the diagonals be x:y=3:2
From this , we have:
[tex]y= \frac{2}{3} y[/tex]
The area of a rhombus, is given by:
[tex] \frac{1}{2} \times product \: of \: diagonals[/tex]
This means:
[tex] \frac{1}{2} xy[/tex]
This is equal to 108 as given in the question.
We substitute to get:
[tex] \frac{1}{2} x \times \frac{2}{3}x = 108 [/tex]
This means:
[tex] {x}^{2} = 324[/tex]
[tex]x = \sqrt{324} =1 8[/tex]
The longest diagonal is 18
