Answer: x=7 and AC = 44 unuts.
Step-by-step explanation:
We know that the diagonals of a parallelogram bisect each other. (i)
Here in parallelogram ABCD , AC and Bd are diagonals intersecting at E.
BE = 2x + 2, BD = 5x – 3, and AE = 4x – 6
Using (i)
![BE=\dfrac{BD}{2}\\\\2x+2=\dfrac{5x-3}{2}\\\\ 2(2x+2)=5x-3\\\\ 4x+4= 5x-3\\\\ 5x-4x=4+3\\\\ x= 7](https://tex.z-dn.net/?f=BE%3D%5Cdfrac%7BBD%7D%7B2%7D%5C%5C%5C%5C2x%2B2%3D%5Cdfrac%7B5x-3%7D%7B2%7D%5C%5C%5C%5C%202%282x%2B2%29%3D5x-3%5C%5C%5C%5C%204x%2B4%3D%205x-3%5C%5C%5C%5C%205x-4x%3D4%2B3%5C%5C%5C%5C%20x%3D%207)
Now , AE = 4(7)-6 = 28-6 = 22
AC =2 AE = 2 (22) =44 units.
Hence, x=7 and AC = 44 unuts.
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