Point B is midpoint of Lince AC.
Given:
AB=2x-1
BC=4x+2
AC=25
Find:
AB and BC
AB + BC = AC
(2x-1)+(4x+2)=25
x=4
AB = 2(4)-1 = 7
BC = 4(4)+2 = 18
To find AB and BC, we can use the information given and the fact that B is the midpoint of line segment AC.
Since B is the midpoint of AC, we can set up the equation AB + BC = AC, where AB and BC are the two segments that make up AC.
From the given information,
AB = 2x - 1
BC = 4x + 2
AC = 25
Now substitute the values of AB and BC into the equation:
(2x - 1) + (4x + 2) = 25
Simplify the equation:
2x - 1 + 4x + 2 = 25
6x + 1 = 25
Subtract 1 from both sides of the equation:
6x = 25 - 1
6x = 24
Divide both sides of the equation by 6:
x = 24 / 6
x = 4
Now that we know the value of x, we can substitute it back into the expressions for AB and BC to find their values:
AB = 2x - 1
AB = 2(4) - 1
AB = 8 - 1
AB = 7
BC = 4x + 2
BC = 4(4) + 2
BC = 16 + 2
BC = 18
Therefore, AB = 7 and BC = 18.