1) x=7 2) x=10
Similar Triangles (SSS) have proportional correspondent sides. So, In the case 1.
1) We can write:
[tex]\begin{gathered} \frac{42}{49}=\frac{8x-2}{63} \\ (8x-2)49=63\cdot42 \\ 392x-98=2646 \\ 392x=2646+98 \\ x=\frac{2646+98}{32} \\ x=7 \end{gathered}[/tex]
For the 2nd pair of triangles, let's evaluate using the same criteria, the proportionality between correspondent sides:
[tex]\begin{gathered} \frac{6x-6}{63}=\frac{42}{49} \\ \frac{6x-6}{63}=\frac{6}{7} \\ 6\cdot63=\text{ 7(6x-6)} \\ 378=42x-42 \\ 420=42x \\ x=\frac{420}{42} \\ x=10 \end{gathered}[/tex]
Notice that a simplification was proceeded on 42/49 dividing both sides by 7.
