In the accompanying diagram of rectangle abcd, diagonal latex: ac=8x+4 a c = 8 x + 4 and diagonal latex: bd=5x+16 b d = 5 x + 16 . find the value of x.

For this case we have the following diagonals:
 AC = 8x + 4
 BD = 5x + 16
 The intersection of the diagonals occurs when:
 AC = BD
 Matching we have:
 8x + 4 = 5x + 16
 Clearing x we have:
 8x-5x = 16-4
 3x = 12
 x = 12/3
 x = 4
 
 the value of x is:
 x = 4