Question

A) For ΔJKL use the Triangle Proportionality Theorem to solve for x.

Answer 1

Answer:

Part a) The value of x is 10

Part b) The perimeter of triangle JKL is $79\ units$

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

$\frac{3x-5}{3x-5+10}=\frac{28-8}{28}\\ \\\frac{3x-5}{3x+5}=\frac{20}{28} \\ \\(3x-5)(28)=(3x+5)(20) \\ \\84x-140=60x+100\\ \\84x-60x=140+100\\ \\24x=240\\ \\x=10$

Part b) we know that

The perimeter of triangle JKL is equal to

$P=JK+KL+JL$

substitute the values

$P=(3x+5)+28+16=3x+49$

substitute the value of x

$P=3(10)+49=79\ units$