Answer:
[tex]1\dfrac{3}{4}\text{ feet}[/tex]
Step-by-step explanation:
From the given information, we have
Total length of board = 8 foot
Length of one piece = [tex]2\dfrac{3}{4}=\dfrac{8+3}{4}=\dfrac{11}{4}[/tex]
Length of second piece = [tex]3\dfrac{1}{2}=\dfrac{6+1}{2}=\dfrac{7}{2}[/tex]
We need to find the length of remaining board.
Length of remaining board = Total length of board - Length of one piece - Length of second piece
[tex]\text{Length of remaining board}=8-\dfrac{11}{4}-\dfrac{7}{2}[/tex]
[tex]\text{Length of remaining board}=\dfrac{32-11-14}{4}[/tex]
[tex]\text{Length of remaining board}=\dfrac{7}{4}=1\dfrac{3}{4}[/tex]
Therefore, the length of remaining board is [tex]1\dfrac{3}{4}\text{ feet}[/tex].
