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I NEED HELP ON THIS BADLY PLEASE!!!! IM GIVING LOTS OF POINTS AND BRAINLIEST!!! This is due today so it would help so so much if someone can help me with this please

I NEED HELP ON THIS BADLY PLEASE IM GIVING LOTS OF POINTS AND BRAINLIEST This is due today so it would help so so much if someone can help me with this please class=

Respuesta :

saItair

Answer :

  • AB = 30

Explanation :

according to the midpoint theorem, In a triangle,the line segment drawn to the other side from one side is parallel and one-half of the third side .

thus,

  • BD = 1/2 AE
  • 3x = 1/2*60
  • 3x = 30
  • x = 30/3
  • x = 10

plugging in the value of x in AC

  • AC = 5x + 10
  • AC = 5*10 + 10
  • AC = 50 + 10
  • AC = 60

since ,the midpoint divides the segment into two equal fraction thus,

  • AB = BC

also,

  • AB + BC = AC
  • 2AB = AC
  • 2AB = 60
  • AB = 60/2
  • AB = 30

thus, AB measures 30 units .

msm555

Answer:

30

Step-by-step explanation:

Given that [tex] \sf B[/tex] is the midpoint of [tex] \sf \overline{AC}[/tex], we can use the Midpoint Segments Theorem:

It states that: "The length of this segment is half the length of the third side."

Let's express [tex] \sf BD[/tex] in terms of [tex] \sf AE[/tex]:

[tex] \sf BD = \dfrac{1}{2}AE[/tex]

Given:

[tex] \sf BD = 3x[/tex]

[tex] \sf AE = 60[/tex]

Now, use the Midpoint Segments Theorem:

[tex] \sf 3x = \dfrac{1}{2}(60)[/tex]

Solve for [tex] \sf x[/tex]:

[tex] \sf 3x = 30[/tex]

[tex]\sf x =\dfrac{30}{3}[/tex]

[tex] \sf x = 10[/tex]

Now that we have the value of [tex] \sf x[/tex], we can find [tex] \sf AB[/tex] using the Segment Addition Postulate:

[tex] \sf AB + BC = AC[/tex]

Substitute the values:

[tex] \sf AB + AB = 5x + 10[/tex]

[tex] \sf 2AB = 5(10) + 10[/tex]

[tex] \sf 2AB = 60[/tex]

[tex]\sf AB =\dfrac{60}{2}[/tex]

[tex] \sf AB = 30[/tex]

Therefore, the length of [tex] \sf AB[/tex] is [tex] \sf 30[/tex].

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