Because JKL and MNP are similar we know that:
[tex] \frac{25}{30}=\frac{20}{4x-4}[/tex].
We can then solve for [tex]x[/tex] as follows:
[tex] \frac{25}{30}=\frac{20}{4x-4}[/tex]
[tex]100x-100=600[/tex]
[tex]100x=700[/tex]
[tex]x=\frac{700}{100}[/tex]
[tex]x=7[/tex]
And the total side length is then:
[tex]4x-4=4(7)-4=28-4=24[/tex]
Which lets us check our work:
[tex]\frac{25}{30}=\frac{20}{24}[/tex]
[tex]\frac{5}{6}=\frac{5}{6}[/tex]
Checks out.
