Given: △ABC, ADEF rhombus D∈AB, E∈BC, F∈AC AB=14, BC=12, AC=10 Find: BE and EC
answer is 7 and 5, its on brainly. don't waste ur answers.
7, 5
To find BE and EC, we can use the properties of a rhombus.
In a rhombus, all sides are congruent, which means DE = EF = FD.
Let's label the length of DE as y. Since DE = FD, we can also say that FD = y.
Now, let's label BE as x and EC as z:
AB = AE + EB
AB = AC - EC
We can substitute the given values:
14 = 10 - EC
EC = 10 - 14
EC = -4
Since the length of a line segment cannot be negative, we can conclude that there may be an error in the problem statement, or further clarification is required to determine the length of EC.
As for BE, we can use the Pythagorean theorem on triangle ADE:
AD^2 + DE^2 = AE^2
AD^2 + y^2 = 14^2
AD^2 + y^2 = 196
To find AD, we can use the Pythagorean theorem on triangle BCD:
BC^2 + CD^2 = BD^2
12^2 + z^2 = BD^2
144 + z^2 = BD^2
Since BD = AD + AB, we can substitute the values:
144 + z^2 = AD^2 + 14^2
144 + z^2 = AD^2 + 196
Now, let's rearrange this equation to isolate z:
z^2 = AD^2 + 196 - 144
z^2 = AD^2 + 52
Now, let's combine the two equations from above:
AD^2 + y^2 = 196
AD^2 + 52 = z^2
Since AD^2 appears in both equations, we can equate them:
196 = z^2 - 52
z^2 = 196 + 52
z^2 = 248
Now, we have two equations:
y^2 + AD^2 = 196
z^2 = 248
We can solve these equations simultaneously to find the values of y and AD. However, without further information or constraints, the specific values of BE and EC cannot be determined.