B is the midpoint of segment AC.
AB= 5X and BC =3X+4
find AB, BC and AC
Since B is the midpoint, the distance AB = BC
5x = 3x+4
x=2
You can probably figure the distances from that.
To find the lengths of segments AB, BC, and AC, we need to solve the given equations using the information that B is the midpoint of segment AC.
Let's start by finding AB:
We are given that AB = 5X.
Next, let's find BC:
We are given that BC = 3X + 4.
Since B is the midpoint of segment AC, it means that the length of segment AB is equal to the length of segment BC.
So, we can set up the equation AB = BC:
5X = 3X + 4
To solve this equation, we can subtract 3X from both sides:
5X - 3X = 3X - 3X + 4
2X = 4
Now, divide both sides by 2:
2X / 2 = 4 / 2
X = 2
Now, substitute the value of X back into the equations to find AB, BC, and AC:
AB = 5X = 5 * 2 = 10
BC = 3X + 4 = 3 * 2 + 4 = 6 + 4 = 10
AC = AB + BC = 10 + 10 = 20
Therefore, the lengths of segments AB, BC, and AC are:
AB = 10
BC = 10
AC = 20
To find the lengths of segments AB, BC, and AC, we will use the information that B is the midpoint of segment AC.
Given:
AB = 5X
BC = 3X + 4
Since B is the midpoint of segment AC, we know that AB is equal to BC. Therefore:
5X = 3X + 4
Now, let's solve the equation for X:
5X - 3X = 4
2X = 4
X = 4/2
X = 2
Now that we have the value of X, we can substitute it back into the expressions for AB and BC to find their values:
AB = 5X = 5 * 2 = 10
BC = 3X + 4 = 3 * 2 + 4 = 6 + 4 = 10
Therefore, we now know the lengths of the segments:
AB = 10
BC = 10
AC = AB + BC = 10 + 10 = 20