Answer:
[tex]x = \dfrac{147}{13}[/tex]
Step-by-step explanation:
Please refer to attached for labeling of the diagram:
We have 2 triangles here in the figure:
[tex]\triangle ABC \text{ and }\triangle BDE[/tex].
1. [tex]\angle B[/tex] is common to both the triangles.
Sides AC || DE (parallel sides):
So, Corresponding angles will be equal
2. [tex]\angle A = \angle D[/tex]
3. [tex]\angle E = \angle C[/tex]
So, [tex]\triangle ABC \text{ and }\triangle BDE[/tex] are similar to each other.
Similar triangles have ratio of their sides as equal.
So, [tex]AB : BD = BC : BE[/tex]
[tex]\Rightarrow \dfrac{6+7}{6} = \dfrac{21}{21-x}\\\Rightarrow \dfrac{13}{6} = \dfrac{21}{21-x}\\\Rightarrow 13 \times (21-x) = 21 \times 6\\\Rightarrow 13x = 7 \times 21\\\Rightarrow x = \dfrac{147}{13}[/tex]
Hence, [tex]x = \dfrac{147}{13}[/tex]
