We are given the triangles:
We know:
AB = 20
BC = 12
DB = 2x + 7
BE = 9
EC = 3
The triangles ABC and DBE are similar, which means, that there is a number k, such that each side of the triangle ABC multiplied by k is equal to the corresponding side in triangle DBE
We can find the number k, using the sides BC and BE:
[tex]k\cdot BC=BE[/tex]
Substitute and solve:
[tex]\begin{gathered} k\cdot12=9 \\ . \\ k=\frac{9}{12} \\ . \\ k=\frac{3}{4} \end{gathered}[/tex]
Now, we can find x because:
[tex]\frac{3}{4}AB=DB[/tex]
Substitute and solve:
[tex]\begin{gathered} \frac{3}{4}\cdot20=2x+7 \\ . \\ 15-7=2x \\ x=\frac{8}{2} \\ . \\ x=4 \end{gathered}[/tex]
The answer is x = 4
