Short Answer 
The SSS similarity theorem states that if the corresponding sides of two triangles are in the same ratio, the triangles are similar. By setting up the equation x/35 = 44/20 and solving for x using cross-multiplication, we find that the value of x that makes the triangles similar is 77.
Step 1: Understanding the SSS Similarity Theorem
The SSS (Side-Side-Side) similarity theorem states that if the three corresponding sides of two triangles are in the same ratio, then those triangles are similar. In simpler terms, if you can find a consistent ratio of the sides of two triangles, they will have the same shape, even if they differ in size. This theorem is crucial for determining similarity in triangles.
Step 2: Setting Up the Equation
In the given problem, we start with the similarity condition for the two triangles: x/35 = 44/20. This sets up a proportion where ‘x’ is the unknown side length that needs to be determined. By recognizing the relationship between the sides, we can work towards finding the value of ‘x’ using cross-multiplication.
Step 3: Solving for x
To isolate ‘x’, we can use the multiplication property of equality. By multiplying both sides of the equation by 35, we derive:
- x = (44 * 35) / 20
- x = 1540 / 20
- x = 77
This leads us to conclude that the value of x which will make the triangles similar is 77.