Answer
The length of the first piece of board is 8 feet.
The length of the second piece of board is 20 feet.
Work Step by Step
Let X represent the length of one piece.
Since the total length of the board was 28, the length of the other piece is 28 - X.
Those lengths are in the ratio of 2 to 5, or $\frac{2}{5}$.
So, let's set up a proportion with the ratio given and a ratio which compares the corresponding lengths.
So, $\frac{2}{5}$ = $\frac{X}{28 - X}$
To solve this equation, we equate the cross products.
2 $\times$ (28 - X) = 5 $\times$ X
56 - 2X = 5X
56 = 7X
Divide both sides by 7
X = 8
The length of the first piece of board is 8 feet.
The length of the second piece of board is 28 - 8 = 20 feet.
