Answer :
The value of x that makes quadrilateral ABCD a rectangle if BE = 3x+1 and ED = 5x-3 is x = 2.
What is a rectangle?
A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
There are four vertices and four sides.
Every vertex has an angle of 90 degrees.
Equal and parallel opposed sides are bisected by a diagonal.
We know that the diagonals of a rectangle bisect each other.
Thus, for the quadrilateral to be a rectangle we have:
BE = ED
3x + 1 = 5x - 3
1 + 3 = 5x - 3x
4 = 2x
x = 2
Hence, the value of x that makes quadrilateral ABCD a rectangle if BE = 3x+1 and ED = 5x-3 is x = 2.
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