Answer:
[tex]\boxed {\boxed {\sf x=42}}[/tex]
Step-by-step explanation:
The 2 triangles have 2 pairs of congruent angles, so they are similar by the angle-angle postulate. Therefore, their sides are proportional.
The bases, x and 30 are proportional.
The sides are proportional. Make sure to add 25 and 10 to find the side length of the larger triangle. So, the proportional sides are 35 and 25.
Now, set up a proportion. Make sure to keep the sides of the same triangle together horizontally across.
[tex]\frac {base_1}{base_2}= \frac{side_1}{side_2}[/tex]
[tex]\frac {x}{30}=\frac {35}{25}[/tex]
Since we are solving for x, we must isolate the variable. It is being divided by 30 and the inverse of division is multiplication. Multiply both sides by 30.
[tex]30*\frac {x}{30}=\frac {35}{25}*30[/tex]
[tex]x=30*1.4\\x=42[/tex]
The side x is equal to 42.
