Question

Point C is on line segment \overline{BD}

BD
. Given CD=2x,CD=2x, BD=3x+4,BD=3x+4, and BC=2x-1,BC=2x−1, determine the numerical length of \overline{BD}.
BD
.​

Answer 1

the numerical length of segment BD is = 19

Explanation:

Given the information that point C is on the segment BD, and understanding that the total segment BD must equal the addition of the two parts on which it is divided by point C, we write the following equation:

BD = BC + CD

now we replace each of the above by their expression in x:

( 3 x + 4 ) = (2 x - 1 ) + (2 x)

and we solve for x in this equation:

3 x + 4 = 2 x + 2 x - 1

3 x +4 = 4 x - 1

4 + 1 = 4 x - 3 x

5 = x

Therefore, we can now obtain the length of segment BD:

BD = 3 x + 4 = 3 (5) + 4 = 15 + 4 = 19