points a b c d and e are collinear in that order . find the length of bc if the length of ac=2x+4, the length of bc = x, the length of bd= 3x+1 an the length of ad=17

Answer 1

Below is the line with the information given from the problem:

2x + 4

l---------------------------------------------------l

--------------------------------------------------------------------------------------

a b c d

l----------------------l

x

l---------------------------------------------------------l

3x + 1

l--------------------------------------------------------------------------------------l

17

To solve, add the value for ac to the value for bd, subtract the value for bc, and set this equal to 17 as follows:

2x + 4 + 3x +1 - x = 17

Combine like terms by adding and subtracting the x's:

4x + 4 + 1 = 17

Next add the numbers on the left side of the equation:

4x + 5 = 17

Solve for x by first subtracting 5 then dividing 4 from both sides:

4x = 12

x = 3

So the length of bc equals 3. You could also solve by first subtracting the value for bc from ab to get ab = x+4, then adding that to bd, which is 3x +1, and you would get the same answer.