Answer: The required value of x is 7.5.
Step-by-step explanation: Given that the triangles shown in the figure are similar by AA similarity postulate.
We are to find the value of x.
We know that the corresponding sides of the similar triangles are proportional.
From the figure, we see that two pairs of corresponding sides in the triangles are (4.5, 3) and (x, 5).
Therefore, we must have
[tex]\dfrac{4.5}{3}=\dfrac{x}{5}\\\\\\\Rightarrow x=\dfrac{4.5\times5}{3}\\\\\Rightarrow x=1.5\times5\\\\\Rightarrow x=7.5.[/tex]
Thus, the required value of x is 7.5.
