Respuesta :
Okay, here we have this:
We obtain the following from the statement:
Width=x
Lenght=3*Width-23=3x-23
[tex]\begin{gathered} Area=Width\cdot Lenght \\ 2870=x\mleft(3x-23\mright) \\ 3x^2-23x=2870 \\ 3x^2-23x-2870=0 \\ x_{1,\: 2}=\frac{-\left(-23\right)\pm\sqrt{\left(-23\right)^2-4\cdot\:3\left(-2870\right)}}{2\cdot\:3} \\ x_{1,\: 2}=\frac{-\left(-23\right)\pm\:187}{2\cdot\:3} \\ x_1=\frac{-\left(-23\right)+187}{2\cdot\:3},\: x_2=\frac{-\left(-23\right)-187}{2\cdot\:3} \\ x_1=35,x_2=-\frac{82}{3} \end{gathered}[/tex]And, as the measure cannot be negative we are left alone with x=35.
This mean that the width is 35feet. Now, let's replace to find the lenght:
Lenght=3*Width-23
Lenght=3*35-23
Lenght=105-23
Lenght=82 feet.
