A is the midpoint of BC. BA=2x+5 and BC=5x-3. solve for x and find the length of BC
Find AC? I assume you have a typo above?
BC = BA + AC
5x - 3 = 2x + 5 + AC
3x - 8 = AC
since A is the MP of BC and BA = 2x + 5
BC = 2(BA)
BC = 2(2x + 5)
BC = 4x + 10
BC = BC
5x - 3 = 4x + 10
x = 13
To solve for x, we can set up an equation using the fact that A is the midpoint of BC.
According to the midpoint formula, the length of BA added to the length of AC should be equal to the length of BC.
So, BA + AC = BC.
Given that BA = 2x + 5 and BC = 5x - 3, we can substitute these values into the equation:
2x + 5 + AC = 5x - 3.
Now, we can solve for x:
2x - 5x = -3 - 5,
-3x = -8,
x = (-8) / (-3),
x = 8/3.
Now that we have found the value of x, we can substitute it back into the equation to find the length of BC:
BC = 5x - 3,
BC = 5 * (8/3) - 3,
BC = 40/3 - 9/3,
BC = (40 - 9) / 3,
BC = 31/3.
Therefore, the length of BC is 31/3.