Since B is the midpoint of AC, we know that AB = BC.
Similarly, since D is the midpoint of CE, we know that CD = DE.
Therefore, AE = AC + CE.
Substituting the given values:
6y + 12 = (AB + BC) + (CD + DE).
Since AB = BC and CD = DE, we can simplify this to:
6y + 12 = 2(AB + CD).
Now, we are given that BD = 2y + 8.
Since AB + BD + CD = AC, we can substitute the given values and expressions:
AB + (2y + 8) + CD = AC.
Since AB = BC and CD = DE, we can rewrite this as:
BC + (2y + 8) + DE = AC.
Therefore, AC = 2(BC + DE).
Since B is the midpoint of AC and D is the midpoint of CE, we can rewrite this as:
AC = 2(BD).
Substituting the given values and expressions:
6y + 12 = 2(2y + 8).
Simplifying this equation:
6y + 12 = 4y + 16.
Subtracting 4y from both sides:
2y + 12 = 16.
Subtracting 12 from both sides:
2y = 4.
Dividing both sides by 2:
y = 2.
Now we can substitute this value back into the equation for BD:
BD = 2(2y + 8) = 2(2(2) + 8) = 2(4 + 8) = 2(12) = 24.
Therefore, BD = 24.
B is the midpoint of AC and D is the midpoint of CE Solve for BD given that BD = 2y + 8 and AE = 6y +12
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