Respuesta :
Let's take l and w as the length and the width of the rectangle.
According to the given information the length is 3 less than twice the width:
[tex]l=2w-3[/tex]And the area, which is the product of the length times the width is 14. Using the equation above, we can re write the formula for the area, this way:
[tex]\begin{gathered} A=w\cdot l \\ 14=w\cdot(2w-3) \\ 14=2w^2-3w \\ 0=2w^2-3w-14 \end{gathered}[/tex]Now, we have to solve the quadratic equation using the quadratic formula:
[tex]\begin{gathered} w=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(2)(-14)}}{2(2)} \\ w=\frac{3\pm\sqrt[]{9+112}}{4} \\ w=\frac{3\pm\sqrt[]{121}}{4} \\ w=\frac{3\pm11}{4} \\ w1=\frac{14}{4}=\frac{7}{2} \\ w2=-\frac{8}{4}=-2 \end{gathered}[/tex]w has 2 values, but for this context, the logic value is 7/2. It means that the width of the rectangle is 7/2.
Now, we can use this value and the first equation to find the length:
[tex]\begin{gathered} l=2w-3 \\ l=2(\frac{7}{2})-3 \\ l=7-3 \\ l=4 \end{gathered}[/tex]The length of the rectangle is 4 and the width is 7/2.
