Question

A is the midpoint of \displaystyle \overline{BC}

BC
. If \displaystyle AB=2x-7AB=2x−7 and \displaystyle CA=5x-22CA=5x−22 , find BC.

Answer 1

Form the Segment Addition Postulate, we know that the length of BC is simply the sum of the lengths of AB and CA. However, first we need to find the value of x in order to find the lengths of AB and CA, so we set up an equation where AB = CA, and solve for it:

5x - 22 = 2x - 7

3x = 15

x = 5

Now we substitute the value of x into the lengths of AB and CA:

AB = 2(5) - 7 = 3

CA = 5(5) - 22 = 3

Next, we add the lengths of AB and CA together to get the length of BC:

AB + CA = BC

3 + 3 = BC

BC = 6

Explanation:

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