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Sagot :
Let 'x' represent the length of the middle piece
We were told that the large piece is 5inches longer than the middle piece,
Mathematically, it means
[tex]x+5[/tex]Also, we were told that the shortest piece is 8inches shorter than the middle piece.
Mathematically, it means
[tex]x-8[/tex]Therefore, the sum of all three lengths must be 48inches.
Hence,
[tex]x+5+x+x-8=48[/tex]Solving for x
[tex]\begin{gathered} x+x+x+5-8=48 \\ 3x-3=48 \\ 3x=48+3 \\ 3x=51 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{3x}{3}=\frac{51}{3} \\ x=17 \\ \therefore The\text{ length of the middle piece=17inches.} \end{gathered}[/tex]Therefore,
The length of the large piece is,
[tex]\begin{gathered} x+5=17+5=22 \\ \therefore The\text{ length of the large piece is 22inches.} \end{gathered}[/tex]The length of the shortest piece is,
[tex]\begin{gathered} x-8=17-8=9 \\ \therefore The\text{ length of the shortest piece is 9inches.} \end{gathered}[/tex]Hence, the lengths of the three-piece are 9inches, 17inches, and 22inches.
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