a)
If the triangles are similar, the corresponding sides vary on the same proportion, so the ratios between the corresponding sides are equal.
For
[tex]\frac{x}{20}=\frac{12}{16}[/tex]
To solve for x you have to multiply both sides of the expression by 20
[tex]\begin{gathered} \frac{20x}{20}=(\frac{12}{16})\cdot20 \\ x=(\frac{3}{4})\cdot20 \\ x=15 \end{gathered}[/tex]
b)
Following the same logic, the ratio between x and 20 is the same as the ratio between 6 and 8
[tex]\frac{x}{20}=\frac{6}{8}[/tex]
6/8 can be simplifies as 3/4. Then multiply both sides by 20 to determine the value of x.
[tex]\begin{gathered} \frac{x}{20}=\frac{6}{8} \\ 20\cdot\frac{x}{20}=(\frac{3}{4})\cdot20 \\ x=15 \end{gathered}[/tex]
As mentioned above, when two triangles are similar, the corresponding sides are always in the same ratio, that is why the results in a and b are the same.
