Question 1151693
let T = the total width of the cabinet.
let S equal the length of the shorter door.
let L equal the length of the longer door.


when the doors are shut, then the overlap is 2/5 * S.
therefore T = S + L - 2/5 * S.
this makes T = 3/5 * S + L


when the doors are open, T = L + 36


since T = L + 36 and T = 3/5 * S + L, then:
L + 36 = 3/5 * S + L
subtract L from both sides of this equation to get:
36 = 3/5 * S
solve for S to get:
S = 5/3 * 36 = 60


when the doors are open, you also get L = S + 1/5 * S.
since S = 60, this means that L = 60 + 12 = 72


you now have S = 60 and L = 72
when the doors are closed, you get T = S + L - 2/5 * S
this becomes T = 60 + 72 - 24.
this makes T = 108


when the doors are open, you get T = L + 36.
since L = 72, this becomes T = 72 + 36
this makes T = 108.


when the doors are open, you get T = S + 1/5 * S + 36
since S = 60, this becomes T = 60 + 12 + 36.
this makes T = 108


the numbers check out.


the length of the shorter door is 60 inches.
the length of the longer door is 72 inches.
the length of the cabinet is 108 inches.


this can be visualized in the following display.


<img src = "http://theo.x10hosting.com/2020/012702.jpg" alt="$$$" >


the very top line that is not labeled was an error and should be ignored.


your solution is that the length of the cabinet is 108 inches.