Question

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.

Answer 1

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