Answer: the correct option is (A) x = y = 2.
Step-by-step explanation: We are given to find the values of x and y that makes the triangles in the figure congruent by HL.
From the figure, we note that
triangles ABC and AED are right-angled triangles with hypotenuse AC, AD and one congruent side BC, ED.
Also, AC = 2x + 3, AD = 3y+1, BC = x and ED = y.
Since the triangles are congruent by HL postulate, so we must have
[tex]x=y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x+3=3y+1~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Substituting the value of x from equation (i) in equation (ii), we get
[tex]2x+3=3x+1\\\\\Rightarrow 3x-2x=3-1\\\\\Rightarrow x=2.[/tex]
So, from equation (i), we arrive at
x = y = 2.
Thus, the correct option is (A).
