The value of x is 5, i.e. option A.
What is a rectangle?
The rectangle is a 2D shape having four sides and the opposite sides of the rectangle are equal and parallel. The sum of all angles of the rectangle is 360°. The diagonals bisect each other, i.e. divides in equal length.
We have,
A quadrilateral ABCD,
And,
The diagonals of quadrilateral intersect at point E,
And,
AE = 5x - 10
And,
EC = 2x + 5
Now,
It is said that the given quadrilateral is a rectangle,
So,
Diagonals of rectangles bisect each other, i.e. divides in equal length.
So,
AE = EC,
Now,
Putting values we get,
5x - 10 = 2x + 5
On solving we get,
5x - 2x = 5 + 10
i.e.
3x = 15
So,
x = 5
Hence, we can say that the value of x is 5, i.e. option A.
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