The two triangles are similar because all the corresponding angles of both triangles are congruent.
To get the scale factor from small to large triangle, the formula is:
[tex]SF=\frac{size\text{ of the large triangle}}{\text{size of the small triangle}}[/tex]
In the small triangle, we have a side that is 5 units long. In the large triangle, the corresponding side is 7 units long. Let's plug these in to the formula above.
[tex]SF=\frac{7}{5}=1.4[/tex]
The scale factor is 7/5 or 1.4.
To determine the value of x, we can still use the formula above.
In the small triangle, we have a side that is 10 units long. In the large triangle, the corresponding side is 10 + x units long. Let's plug these into the scale factor formula.
[tex]\begin{gathered} 1.4=\frac{10+x}{10} \\ 14=10+x \\ x=14-10 \\ x=4 \end{gathered}[/tex]
Therefore, the value of x is 4.
