Respuesta :
So, we have AB that is 3x-1 and the entire segment AC that is 8x-20
Now, if B is the midpoint, B divides perfectly in half the segment.
AB is as long as BC.
And if you add up AB and BC you get AC.
First of all, BC is our unknown measure.
AB + BC = AC
3x - 1 + BC = 8x - 20
BC = 8x - 20 - (3x - 1)
BC = 8x - 20 - 3x + 1
BC = 5x - 19
We have finally found BC
BC is equal to AC and we can use this formula to find x.
5x - 19 = 3x - 1
5x - 3x = -1 + 19
2x = 18
x = 9
Plug in the value 9.
BC = 5(9) - 19 = 45 - 19 = 26
Answer is BC = 26
Now, if B is the midpoint, B divides perfectly in half the segment.
AB is as long as BC.
And if you add up AB and BC you get AC.
First of all, BC is our unknown measure.
AB + BC = AC
3x - 1 + BC = 8x - 20
BC = 8x - 20 - (3x - 1)
BC = 8x - 20 - 3x + 1
BC = 5x - 19
We have finally found BC
BC is equal to AC and we can use this formula to find x.
5x - 19 = 3x - 1
5x - 3x = -1 + 19
2x = 18
x = 9
Plug in the value 9.
BC = 5(9) - 19 = 45 - 19 = 26
Answer is BC = 26
The measure of BC is 26.
Given:
B is be midpoint of AC.
[tex]AC=8x-20[/tex]
[tex]AB= 3x-1[/tex]
To find:
The measure of BC.
Solution:
If B is be midpoint of AC, it means the point B divides the line segment AC in two equal parts. So, the measure of AB and the measure BC are equal to half of the measure of AC.
[tex]AB=BC[/tex] ...(i)
And,
[tex]BC=\dfrac{AC}{2}[/tex]
[tex]BC=\dfrac{8x-20}{2}[/tex]
[tex]BC=\dfrac{8x}{2}-\dfrac{20}{2}[/tex]
[tex]BC=4x-10[/tex] ...(ii)
Using (i) and (ii), we get
[tex]AB=4x-10[/tex]
Substituting the given value of AB, we get
[tex]3x-1=4x-10[/tex]
[tex]3x-4x=1-10[/tex]
[tex]-x=-9[/tex]
[tex]x=9[/tex]
Substituting [tex]x=9[/tex] in (ii), we get
[tex]BC=4(9)-10[/tex]
[tex]BC=36-10[/tex]
[tex]BC=26[/tex]
Therefore, the measure of BC is 26.
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