Answer:
Part a) The value of x is 10
Part b) The perimeter of triangle JKL is [tex]79\ units[/tex]
Step-by-step explanation:
Part a) Find the value of x
we know that
The Triangle Proportionality Theorem, states that if a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally
[tex]\frac{3x-5}{3x-5+10}=\frac{28-8}{28}\\ \\\frac{3x-5}{3x+5}=\frac{20}{28} \\ \\(3x-5)(28)=(3x+5)(20) \\ \\84x-140=60x+100\\ \\84x-60x=140+100\\ \\24x=240\\ \\x=10[/tex]
Part b) we know that
The perimeter of triangle JKL is equal to
[tex]P=JK+KL+JL[/tex]
substitute the values
[tex]P=(3x+5)+28+16=3x+49[/tex]
substitute the value of x
[tex]P=3(10)+49=79\ units[/tex]
