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 Answer: the value of x is: x = 4
