Question

What value of x would make KM ∥ JN?

Triangle J L N is cut by line segment K M. Line segment K M goes from side J L to side L N. The length of J K is x minus 5, the length of K L is x, the length of L M is x + 4, and the length of M N is x minus 3.


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

What value of x would make KM ∥ JN?

Triangle J L N is cut by line segment K M. Line segment K M goes from side J L to side L N. The length of J K is x minus 5, the length of K L is x, the length of L M is x + 4, and the length of M N is x minus 3.

Complete the statements to solve for x.

By the converse of the side-splitter theorem, if JK/KL =

✔ NM/ML

, 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 + 4

) = x(x – 3).

Distribute: x(x) + x(4) – 5(x) – 5(4) = x(x) + x(–3).

Multiply and simplify: x2 – x –

✔ 20

= x2 – 3x.

Solve for x: x =

✔ 10

.Step-by-step explanation:

Answer 2

x = 10

Explanation:

By the converse of the side-splitter theorem, if
`(JK)/(KL)= (NM)/(ML)` , then KM ∥ JN.

Substitute the expressions into the proportion:

`(x-5)/(x)= (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.