ABCD is a parallelogram with diagonals intersecting at E. If AE = 3x + 12 and EC = 27, find the value of x.
The answer's 5
Well, ABCD is a parallelogram, so its diagonals bisect each other. That means that AE = EC. So if AE is 3x + 12 and EC is 27, then we can set up an equation:
3x + 12 = 27
Now, let me run it through my hilarious equation-solving algorithm to find the value of x:
3x = 27 - 12
3x = 15
x = 5
Voila! The value of x is 5. And that's no joke! Well, maybe it is a little bit of one, but still... it's the right answer!
To find the value of x, we need to use the given information about the parallelogram ABCD. Let's look at the diagonals.
In a parallelogram, the diagonals bisect each other. So, we can assume that AE is equal to EC, since they are the two halves of the diagonal. This allows us to set up an equation:
AE = EC
Substituting in the given values:
3x + 12 = 27
Now we can solve the equation for x. First, let's isolate the variable term. We can do this by subtracting 12 from both sides of the equation:
3x = 27 - 12
3x = 15
Next, we can solve for x by dividing both sides of the equation by 3:
x = 15 / 3
x = 5
Therefore, the value of x is 5.
17
since the diagonals bisect each other,
AE = EC
3x+12 = 27
...