The quadrilateral ABCD was dilated by a scale factor of 3/4 to form the quadrilateral A'B'C'D'
This means that each side of the quadrilateral was multiplied by 3/4 to make the dilation.
You know that the scale factor is 3/4 and the length of D'A' is equal to 30 units, then:
[tex]\begin{gathered} D^{\prime}A^{\prime}=\frac{3}{4}DA \\ 30=\frac{3}{4}DA \end{gathered}[/tex]
Multiply both sides by the reciprocal of 3/4
[tex]\begin{gathered} 30\cdot\frac{4}{3}=(\frac{4}{3}\cdot\frac{3}{4})DA \\ 40=DA \end{gathered}[/tex]
The length of side DA is 40 units.
