In quadrilateral abcd, ae=x+10, and be=3x-18. for what value of x is abcd a rectangle? a.24 b.14 c.18 d.16

for x  = 14, the given ABCD is a RECTANGLE.

Step-by-step explanation:

Given : ABCD is  a quadrilateral.

E is the intersection points of the diagonal AC and BD.

AE  =  x+10, and BE=  3x -18

Now, as we know:

IN A RECTANGLES , DIAGONALS BISECT EACH OTHER.

⇒  E is the mid point of AC and BD respectively.

⇒ AE = BE

⇒ x+10 = 3 x - 18

or, 10 +  18 = 3 x - x

or, 2  x = 28

or, x  = 28/2 = 14   ⇒  x = 14

Hence, for x  = 14, the given ABCD is a RECTANGLE.

a

step-by-step explanation: