Question

Complete the statements to solve for x. By the converse of the side-splitter theorem, if JK/KL = , then KM ∥ JN. Substitute the expressions into the proportion: StartFraction x minus 5 Over x EndFraction = StartFraction x minus 3 Over x 4 EndFraction. Cross-multiply: (x – 5)( ) = x(x – 3). Distribute: x(x) x(4) – 5(x) – 5(4) = x(x) x(–3). Multiply and simplify: x2 – x – = x2 – 3x. Solve for x: x =.

Answer 1

The value of x is 10.

Given

By the converse of the side-splitter theorem;

If  $\rm \dfrac{JK}{KL}$ then, KM||JN.

What is the side-splitter theorem?

If a line is parallel to one side of the triangle and intersects the other 2 sides, it divides the sides proportionally.

If a line is drawn parallel to one side of the triangle, then it divides the other two sides in the same ratio.

KM || JN

$\rm \dfrac{JK}{KL}= \dfrac{NM}{ML}$

Where JK = x-5, KL = x-3, NM = x, and KL = x+4.

Substitute all the values in the equation

$\rm \dfrac{JK}{KL}= \dfrac{NM}{ML}\\\\ \dfrac{x-5}{x-3} = \dfrac{x}{x+4}\\\\(x-5) (x+4) = x(x-3)\\\\x^2+4x-5x-20 = x^2-3x\\\\x^2-x-20-x^2+3x=0\\\\2x-20=0\\\\2x = 20\\\\x = \dfrac{20}{2}\\\\x=10$

Hence, the value of x is 10.

To know more about the side-splitter theorem click the link given below.

https://brainly.com/question/10612748