Question

What value of x would make KM ∥ JN?

Answer 1

Answer:

x = 10

Step-by-step explanation:

By the converse of the side-splitter theorem, if $\dfrac{JK}{KL}= \dfrac{NM}{ML}$ , then KM ∥ JN.

Substitute the expressions into the proportion:

$\dfrac{x-5}{x}= \dfrac{x-3}{x+4}$

Cross-multiply:

(x – 5)(x+4) = x(x – 3).

Distribute:

$x(x) + x(4) - 5(x) - 5(4) = x(x) + x(-3).$

Multiply and simplify:

$x^2 +4x- 5x - 20 = x^2-3x\\-x-20=-3x\\ Collect like terms \\-x+3x=20\\2x=20\\ Divide both sides by 2\\x=10$

Solve for x: x = 10

Therefore, the value of x that would make KM parallel to JN is 10.