Answer:
x = 10
Step-by-step explanation:
By the converse of the side-splitter theorem, if [tex]\dfrac{JK}{KL}= \dfrac{NM}{ML}[/tex] , then KM ∥ JN.
Substitute the expressions into the proportion:
[tex]\dfrac{x-5}{x}= \dfrac{x-3}{x+4}[/tex]
Cross-multiply:
(x – 5)(x+4) = x(x – 3).
Distribute:
[tex]x(x) + x(4) - 5(x) - 5(4) = x(x) + x(-3).[/tex]
Multiply and simplify:
[tex]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[/tex]
Solve for x: x = 10
Therefore, the value of x that would make KM parallel to JN is 10.
Answer:
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:
