SOLUTION: In quadrilateral ABCD, AE = x + 2, and BE + 3x – 18. For what value of x is ABCD a rectangle?

Algebra ->  Parallelograms -> SOLUTION: In quadrilateral ABCD, AE = x + 2, and BE + 3x – 18. For what value of x is ABCD a rectangle?       Log On


   

Question 686988: In quadrilateral ABCD, AE = x + 2, and BE + 3x – 18. For what value of x is ABCD a rectangle?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
In quadrilateral ABCD,
given:
AE+=+x+%2B+2, and
BE+=3x+-18
find: For what value of x is ABCD a rectangle?




The diagonals of a rectangle are congruent; so
AC=BD
AC=2AE+=+2%28x+%2B+2%29=2x%2B4
BD=2BE+=2%283x-18%29=6x-36

than
2x%2B4=6x-36......solve for x
36%2B4=6x-2x
40=4x
highlight%2810=x%29