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.

Given that the third is 7 cm longer than the second.

Substitute b=2a, we get

The sum of the three pieces =The length of the board.

Substitute b=2a and c=2a+7, we get


Subtracting 7 from both sides, we get


Dividing both sides by 5, we get


Substitute a=14cm in b=2a and c=2a+7, we get


Hence the length of the shorter piece is 14cm.