Question

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

b) After you have solved for x, what is the Perimeter of ΔJKL?


(SHOW ALL YOUR WORK)

Answer 1

Part a) The value of x is 10

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

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

`(3x-5)/(3x-5+10)=(28-8)/(28)\\ \\(3x-5)/(3x+5)=(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`