B is the midpoint of a AC and D is the midpoint of CE solve for BD given that BD = 2Y + 8 and AE = 6Y +12
Since B is the midpoint of AC, we can write the equation:
AC = 2AB
Since D is the midpoint of CE, we can write the equation:
CE = 2CD
We also know that AC = AE + EC.
Substituting the given values, we get:
2AB = 6Y + 12 + 2CD
Rearranging the equation, we get:
2CD = 2AB - 6Y - 12
Since B is the midpoint of AC, AB = BC.
Plugging this into the equation, we get:
2CD = 2BC - 6Y - 12
Since D is the midpoint of CE, CD = DE.
Plugging this into the equation, we get:
2DE = 2BC - 6Y - 12
Since AB + BC = AC, we can substitute AB = AC/2 and BC = AC/2 into the equation:
2DE = AC - 6Y - 12
Since AC = 2AB, we can substitute AC = 2(BC) into the equation:
2DE = 2(BC) - 6Y - 12
2DE = 2BC - 6Y - 12
But we already know that 2CD = 2BC - 6Y - 12.
Therefore, 2DE = 2CD.
This means that DE = CD.
Since D is the midpoint of CE, we know that EC = 2CD.
We can substitute EC = 2CD into the equation:
2DE = EC
DE = EC/2
Finally, since D is the midpoint of CE, we can write the equation:
DE = (CE + EC)/2
Substituting the given values, we get:
DE = (6Y + 12 + 2CD)/2
Substituting CD = DE, we get:
DE = (6Y + 12 + 2DE)/2
Multiplying both sides of the equation by 2, we get:
2DE = 6Y + 12 + 2DE
Simplifying the equation, we get:
DE = 3Y + 6
So, BD = 2(3Y + 6) + 8
BD = 6Y + 12 + 8
BD = 6Y + 20