Hi,

Let x represent length of the shorter piece

then (21ft -x) would represent the lomger piece

Question states***

5x = 3(21ft-x) +1ft

solving for x

5x = 63ft - 3x + 1ft

8x = 64ft

x = 8 ft, the length of the shorter piece

Longer piece is 13ft  (21ft-8ft)

CHECKING our Answer***

5*8ft = 3*13ft + 1ft = 40ft 

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