Answer: The required value of x is 4.
Step-by-step explanation: We are given that the triangles ABC and IGH congruent by HL, where
AB = 9 units, BC = 12 units, AC = 15 units, IH = 3x + 3 and IG = 2x + 1.
We are to find the value of x.
Since the triangles ABC and IGH are congruent by HL rule, so we have
[tex]AB=IG,\\\\AC=IH.[/tex]
That is,
[tex]AC=IH\\\\\Rightarrow 15=3x+3\\\\\Rightarrow 3x=15-3\\\\\Rightarrow 3x=12\\\\\Rightarrow x=\dfrac{12}{3}\\\\\Rightarrow x=4.[/tex]
Thus, the required value of x is 4.
