Answer:
[tex]x=4[/tex]
Step-by-step explanation:
We have been given two right triangles. We are asked to find the value of x, which will make both triangles similar by Hypotenuse-Leg congruence.
Hypotenuse-Leg theorem states if one leg and hypotenuse of a right triangle is congruent to the one leg and hypotenuse of other right triangle, then both triangles are congruent.
So we can set an equation as:
[tex]2x+1=9[/tex]
Upon subtracting 1 from both sides we will get,
[tex]2x+1-1=9-1[/tex]
[tex]2x=8[/tex]
Dividing both sides of our equation by 2 we will get,
[tex]\frac{2x}{2}=\frac{8}{2}[/tex]
[tex]x=4[/tex]
Therefore, the value of x equals 4 will make both triangles congruent by HL theorem.
