B is the midpoint of AC, D is the midpoint of CE, and Bd=14. find AE.
B is the midpoint of AC, D is the midpoint of CE and BD=7. Find AE.
Just lay out the points on the line
BD contains the right half of BC and the left half of CE
So, what's left is the same length: The left half of AC and the right half of CE
AE = AB + BC + CD + DE
but BD = BC + CD = 14
so,
AE = AB + 14 + DE
However,
AB = BC and CD = DE so AB+DE = BC+CD = 14
AE = 14 + 14 = 28
With that in hand, the 2nd problem should be trivial.
To find the length of AE, we can use the property of midpoints which states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.
Since B is the midpoint of side AC, we can deduce that AB = BC. Similarly, since D is the midpoint of side CE, we can conclude that CD = DE.
Given that BD = 14, we can determine that BC = CD = 14/2 = 7.
Now, we know that AB = BC = CD = 7.
To find AE, we need to determine the length of AD. Since D is the midpoint of side CE, we can conclude that AD = (1/2) * CE.
Using the information provided, we noted that CD = DE. Since CD = 7, we can infer that DE = 7.
Substituting this value into the equation, we find AD = (1/2) * 7 = 7/2.
Finally, to find AE, we add AD and DE: AE = AD + DE = 7/2 + 7 = 7/2 + 14/2 = 21/2.
Therefore, AE = 21/2 or 10.5 units.