Question

WILL GIVE BRAINLIEST!!!

Answer 1

ABCD - rectangle,  AC ∩ BD = {E}

The diagonals of the rectangle are equal, so their halves will be equal.

AC = BD ⇒ DE = AE ⇒ 5x-7 = 3x - 1 ⇒ 5x - 3x = 7-1 ⇒ 2x = 6 ⇒ x = 3     (1)

AC = 2·AE = 2·(3x-1) = 6x - 2      (2)

AC = 6·3 - 2 = 18 - 2 = 16.

Answer 2

If E is in the center of the rectangle, AE = DE, so
.. 3x -1 = 5x -7
.. 6 = 2x . . . . . . . add 7-3x
.. x = 3

AE = 3*3 -1 = 8
If E is in the center of the rectangle, this distance is half the length of the diagonal, so
.. the diagonal is 2*8 = 16 . . . . . . . . corresponding to the 3rd selection