Question

I can’t figure mid segments out! Help please.

Triangle ABC has the mid segment DE, where D is the midpoint of AB and E is the midpoint of AC. The lengths of AD and DB are given below. What is the length of AB?

AD= x^2 - x + 2
DB = x^2 - 2x + 6

Answer 1

AB = 28

Explanation:

A midsegment joins midpoints of sides of the figure. In this problem, the midsegment is irrelevant.

What is important is that D is the midpoint of AB. That means ...

AD = DB

x^2 -x +2 = x^2 -2x +6

x = 4 . . . . . . . add 2x -2 -x^2 to both sides

The length of AD is then ...

AD = x^2 -x +2 = 4^2 -4 +2 = 16 -4 +2 = 14

AD is half the length of AB, so ...

AB = 28