B is the midpoint of line AC. If AB = 12x-5 and BC = 4x + 15. Find x and BC.
since B is the midpoint of line AC, that means AB=BC
set AB=BC
12x-5=4x+15
find x. plug x into 4x+15 to find BC.
To find x and BC, we can use the fact that B is the midpoint of line AC. The midpoint of a line segment divides it into two equal parts. Therefore, we can set up an equation using the lengths of AB and BC:
AB = BC
Given that AB = 12x-5 and BC = 4x + 15, we can substitute these expressions into the equation:
12x-5 = 4x + 15
Now we can solve for x. First, let's simplify the equation by combining like terms:
12x - 4x = 15 + 5
8x = 20
Next, we isolate x by dividing both sides of the equation by 8:
x = 20/8
Simplifying the fraction gives:
x = 2.5
So we have found the value of x. To find BC, we can substitute this value back into the expression for BC:
BC = 4(2.5) + 15
BC = 10 + 15
BC = 25
Therefore, we have found that x = 2.5 and BC = 25.