Let's use the variable L to represent the length and W to represent the width.
If the length is 3 yd less than double the width, we can write the following equation:
[tex]L=2W-3[/tex]
If the area is equal to 14 yd², we have this equation:
[tex]L\cdot W=14[/tex]
Let's use the value of L from the first equation into the second one, then we solve the resulting equation for W:
[tex]\begin{gathered} (2W-3)\cdot W=14 \\ 2W^2-3W=14 \\ 2W^2-3W-14=0 \\ W=\frac{-(-3)\pm\sqrt[]{(-3)^2-4\cdot2\cdot(-14)}}{2\cdot2} \\ W=\frac{3\pm\sqrt[]{9+112}}{4} \\ W=\frac{3\pm11}{4} \\ W_1=\frac{3+11}{4}=\frac{14}{4}=3.5 \\ W_2=\frac{3-11}{4}=-\frac{8}{4}=-2 \end{gathered}[/tex]
Since a negative value for the width is not valid, we have W = 3.5 yd.
Now, calculating the length, we have:
[tex]\begin{gathered} L=2W-3 \\ L=2\cdot3.5-3 \\ L=7-3 \\ L=4\text{ yd} \end{gathered}[/tex]
Therefore the length is 4 yards and the width is 3.5 yards.
