Respuesta :
The formula for calculate the area of a rectangle is:
[tex]A=lw[/tex]Where "l" is the length and "w" is the width,
According to the information given in the exercise:
[tex]\begin{gathered} l=2w+5 \\ A=42 \end{gathered}[/tex]Then, you can set up the following equation:
[tex]42=(2w+5)(w)[/tex]Simplify it:
[tex]42=2w^2+5w[/tex]Make it equal to zero:
[tex]2w^2+5w-42=0[/tex]Use the Quadratic formula to find the value of "w":
[tex]w=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case:
[tex]\begin{gathered} a=2 \\ b=5 \\ c=-42 \end{gathered}[/tex]Substituting values and evaluating, you get:
[tex]\begin{gathered} w=\frac{-5\pm\sqrt[]{5^2^{}-4(2)(-42)}}{2(2)} \\ \\ w_1=3.5 \\ w_2=-6 \end{gathered}[/tex]Choose the positive value. Then:
[tex]w=3.5ft[/tex]Substitute the width into the equation
[tex]l=2w+5[/tex]And then evaluate, in order to find the length of the rectangle. This is:
[tex]\begin{gathered} l=2(3.5)+5 \\ l=12ft \end{gathered}[/tex]The answer is:
[tex]\begin{gathered} l=12ft \\ w=3.5ft \end{gathered}[/tex]