The midsegment of triangle ABC is LM. What is the length of AC if LM is 15 inches long?

It is given that The mid segment of triangle ABC is LM. We know that A midsegment is the line segment connecting the midpoints of two sides of a triangle. A triangle midsegment is parallel to the third side of the triangle and is half of the length of the third side.

Consider triangle ABC and LM is the midsegment of this triangle. Then, according to the definition of mid segment, we have:

[tex]LM=\frac{AC}{2}[/tex]

⇒[tex]15=\frac{AC}{2}[/tex]

⇒[tex]AC=15{\times}2[/tex]

⇒[tex]AC=30inches[/tex]

Thus, the length of AC is 30 inches.

Lanuel Lanuel · Answer 2 · 2022-07-16T02:07:21+02:00

By applying the triangle midpoint theorem to triangle ABC, the length of AC is equal to 30 inches.

What is triangle midpoint theorem?

Triangle midpoint theorem states that the line segment which connects the midpoints of two sides of a triangle is parallel to the third side, and it's congruent to one-half of the third side.

By applying the triangle midpoint theorem to triangle ABC, the length of LM is given by:

LM = AC/2

Since LM = 15, we have:

15 = AC/2

Cross-multiplying, we have:

AC = 15 × 2

AC = 30 inches.

Read more on triangle midpoint theorem here: https://brainly.com/question/7131495

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