x = 11
Solution:
To find the value of x:
Property of similar polygon:
If two polygons are similar, then their corresponding angles are equal and the lengths of the corresponding sides are in proportion.
[tex]$\Rightarrow\frac{6}{2x-8} =\frac{9}{21}[/tex]
Do cross multiplication.
[tex]\Rightarrow6\times21=(2x-8)\times9[/tex]
[tex]\Rightarrow 126=18x-72[/tex]
Add 72 on both side of the equation.
[tex]\Rightarrow 126+72=18x-72+72[/tex]
[tex]\Rightarrow 198=18x[/tex]
Divide by 18 on both side of the equation.
[tex]\Rightarrow 11=x[/tex]
⇒ x = 11
Hence the value of x is 11.
