The Varignon parallelogram of the Varignon parallelogram of quadrilateral ABCD is a 3*4 rectangle. Find AC+BD.
I don't understand the Varignon parallelogram, so solving this problem is difficult.
Good link here:
https://en.wikipedia.org/wiki/Varignon's_theorem
contains a proof which is easy to follow
Shut up dweeb and study U fool
No worries! Let me explain the concept of the Varignon parallelogram to you.
The Varignon parallelogram is created by connecting the midpoints of the sides of a given quadrilateral. In other words, for quadrilateral ABCD, you would find the midpoints of sides AB, BC, CD, and AD, and then connect these midpoints to form a new parallelogram.
To solve the problem, we need to use the properties of the Varignon parallelogram. One important property is that the diagonals of the Varignon parallelogram are parallel to the diagonals of the original quadrilateral and are half their length.
To determine the length of AC and BD, we need to find the length of the diagonals of the Varignon parallelogram. Given that the Varignon parallelogram is a 3*4 rectangle, we can use the Pythagorean theorem to find the length of the diagonals.
Let's call the length of AC diagonal 'd1' and the length of BD diagonal 'd2'.
Using the Pythagorean theorem, we have:
d1^2 = 3^2 + 4^2
d1^2 = 9 + 16
d1^2 = 25
d1 = √25
d1 = 5
Similarly,
d2^2 = 3^2 + 4^2
d2^2 = 9 + 16
d2^2 = 25
d2 = √25
d2 = 5
Now, since the diagonals of the Varignon parallelogram are half the length of the diagonals of the original quadrilateral, we can say:
AC = 2 * d1 = 2 * 5 = 10
BD = 2 * d2 = 2 * 5 = 10
Therefore, AC + BD = 10 + 10 = 20.
So, the answer is 20.