Suppose B is the midpoint of AC. AB = 5x and BC = 3x + 4. Find AB.
5x=3x+4
Subtract 3x from both sides.
Divide both sides by 2.
To find the length of AB, we can use the fact that B is the midpoint of AC. This means that the length of AB is equal to the length of BC.
We are given that AB = 5x and BC = 3x + 4. Since B is the midpoint of AC, AB must be equal to BC. So, we can set up the equation:
5x = 3x + 4
To solve for x, we will isolate the variable by subtracting 3x from both sides of the equation:
5x - 3x = 4
Simplifying the equation:
2x = 4
Next, we need to solve for x by dividing both sides of the equation by 2:
2x / 2 = 4 / 2
Simplifying:
x = 2
Now that we have found the value of x, we can substitute it back into the equation for AB:
AB = 5x
AB = 5(2)
AB = 10
Therefore, the length of AB is 10.