Question

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.

Answer 1

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

Answer 2

x=15

Explanation:

In a rectangle you always have that the diagonals are congruent, so they must measure the same, i.e. DT=AE=40.

On the other hand the point S is the mid point of DT, so ST=20.

then we have

20=ST=x+5

and hence

x=20-5=15