Question

In -ABC, D is the midpoint of BC . If BD= 4x + 12 and CD = 2x + 32,
what is the length of BC?

Answer 1

9514 1404 393

Answer:

104

Explanation:

The midpoint divides the segment into equal parts:

BD = CD

4x +12 = 2x +32

2x = 20 . . . . . . . . . subtract 2x+12

x = 10 . . . . . . . . divide by 2

The length of BC is the sum of the segment lengths:

BC = BD +CD

BC = (4x +12) +(2x +32) = 6x +44

For x=10, this is ...

BC = 6(10) +44 = 104

The length of BC is 104 units.