The boards to be selected are as follows;
[tex]1\frac{1}{2}\text{ ft , 2}\frac{1}{4}\text{ ft , 1}\frac{3}{4}\text{ ft ,4}\frac{1}{3}\text{ ft , 2}\frac{2}{3}\text{ ft}[/tex]Here,we have that five boards are needed
So, what we have to do here is to add 5 boards which length sum would be equal to 12 1/2 ft
We have this as follows;
[tex]1\frac{1}{2}\text{ ft + 2}\frac{1}{4}\text{ ft + 1}\frac{3}{4}\text{ ft + 4}\frac{1}{3}\text{ ft + 2}\frac{2}{3}\text{ ft = 12}\frac{1}{2}\text{ ft}[/tex]