Given:
The length of the board is 77 cm.
Let a be the length of the first piece.
Let b be the length of the second piece.
Let c be the length of the third piece.
Given that the second piece is twice as long as the first.
[tex]b=2a[/tex]Given that the third is 7 cm longer than the second.
[tex]c=b+7[/tex]Substitute b=2a, we get
[tex]c=2a+7[/tex]The sum of the three pieces =The length of the board.
[tex]a+b+c=77[/tex]Substitute b=2a and c=2a+7, we get
[tex]a+2a+2a+7=77[/tex][tex]5a+7=77[/tex]Subtracting 7 from both sides, we get
[tex]5a+7-7=77-7[/tex][tex]5a=70[/tex]Dividing both sides by 5, we get
[tex]\frac{5a}{5}=\frac{70}{5}[/tex][tex]a=14cm[/tex]Substitute a=14cm in b=2a and c=2a+7, we get
[tex]b=2\times14=28cm[/tex][tex]c=2\times14+7=35cm[/tex]Hence the length of the shorter piece is 14cm.
