[tex]\Delta KLJ\sim\DeltaNPM[/tex] (AAA) Corresponding angles are congruent.
Therefore, the sides of the triangles are proportional:
[tex]\dfrac{4x-4}{20}=\dfrac{30}{25}[/tex] cross multiply
[tex]25(4x-4)=(20)(30)[/tex] use distributive property
[tex](25)(4x)+(25)(4)=600\\\\100x+100=600[/tex] subtract 100 from both sides
[tex]100x=500[/tex] divide both sides by 100
[tex]x=5[/tex]
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[tex]\Delta PQR\cong\Delta STU[/tex] (SAS)
If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.
Therefore we have the equation:
[tex]3y-2=y+4\qquad|+2\\\\3y=y+6\qquad|-y\\\\2y=6\qquad|:2\\\\y=3[/tex]
The perimeter of △PQR:
[tex]P=4+6+3y-2=8+3y[/tex]
Substitute the value of y to the expression:
[tex]P=8+3(3)=8+9=17\ ft[/tex]
