In rectangle DATE, the diagonals DT and AE intersect as S. If LaTeX: AE=40 A E = 40 and LaTeX: ST=x+5 S T = x + 5 , find the value of x.

For this case we have the following diagonals:
 AE = 40
 ST = x + 5
 The intersection of the diagonals occurs when:
 AE = ST
 Therefore, matching we have:
 40 = x + 5
 Clearing x we have:
 x = 40-5
 x = 35
 Answer:
 The value of x is:
 x = 35