Let the smaller piece be x .
Then the larger angle will be = 3x
An equation to find the length of each of the two pieces :-
[tex]x + 3x = 112[/tex]
[tex]4x = 112[/tex]
[tex]x = \frac{112}{4} [/tex]
[tex]x = 28[/tex]
Which means :-
Length of the shorter piece = 28 inches
Length of the larger piece = 28 × 3 = 84 inches
Therefore , the length of the shorter piece = 28 inches .