If b is the midpoint of ac, ac=cd, ab=3x+4, ac=11x-17, and ce=49, find de

The measure of segment DE is 11.

Given:

See image in the attachment below showing the information given in the question.

Since B is the midpoint of AC, therefore:

Substitute

Solve for x

Divide both sides by 5

Find DE:

(Segment Addition Postulate)

Plug in the value of x

Substitute

Therefore the length of DE = 11.

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de=11

Step-by-step explanation:

We are given that b is the midpoint of ac

ac=cd, ab=3x+4,ac=11x-17 and ce=49

We have to find the value of de

b is the midpoint of ac therefore we have

ab=bc

ac=ab+bc=ab+ab=2ab

Then , substitute the value of x

ac=

ce=cd+de

49=38+de

de=11

.

step-by-step explanation: