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Korvikt [17]
1 year ago
8

Triangle A C B is cut by line segment E D. Line segment E D goes from side B C to side A C. The length of B A is 4 x minus 6 and

the length of E D is x + 2. The length of B E is x. Sides B E and E C are congruent. Sides A D and D C are congruent.
What is the length of BC?

From the markings on the diagram, we can tell E is the midpoint of BC and

is the midpoint of AC

We can apply the

theorem: ED = One-halfBA.

Substituting in the expressions for the lengths and solving for x, we get x =

.

Now, since BE = x, then BC =
.
Mathematics
1 answer:
bezimeni [28]1 year ago
6 0

From the markings on the diagram, we can tell E is the midpoint of BC and <u>D</u> is the midpoint of AC. We can apply the <u>triangle midsegment theorem</u>: ED = ½BA. Substituting in the expressions for the lengths and solving for x, we get x = <u>5</u>. Now, since BE = x, then BC = <u>10</u>.

<h3>What is triangle midpoint theorem?</h3>

Triangle midpoint theorem states that the line segment which joins the midpoints of two (2) 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, we can find the value of x:

ED = ½BA

x + 2 = ½(4x - 6)

2x + 4 = 4x - 6

4x - 2x = 6 + 4

2x = 10

x = 10/2

x = 5.

BC = x + x

BC = 5 + 5

BC = 10.

Read more on triangle midpoint theorem here: brainly.com/question/16047906

#SPJ1

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