Respuesta :
Let's take the length as x and the width as y.
According to the statement, the width is 6 less than the length, it means the width is x-6. It is also said that the area is 135, it means that the width times the length is 135.
Use this information to find the length and the width.
[tex]y=x-6[/tex][tex]\begin{gathered} A=x\cdot y=135 \\ x\cdot(x-6)=135 \end{gathered}[/tex]Write the quadratic equation:
[tex]x^2-6x-135=0[/tex]Solve for x (use the quadratic formula):
[tex]\begin{gathered} x_{}=\frac{-\left(-6\right)\pm\sqrt{\left(-6\right)^2-4\cdot\:1\cdot\left(-135\right)}}{2\cdot\:1} \\ x_{}=\frac{-\left(-6\right)\pm\:24}{2\cdot\:1} \\ x_{}=\frac{-\left(-6\right)+24}{2\cdot\:1},\: x_{}=\frac{-\left(-6\right)-24}{2\cdot\:1} \\ x=15 \\ x=-9 \end{gathered}[/tex]In this case, we have to use only positive values of x, because the length of a rectangle can not be negative. It means, the length of the rectangle is 15 and the width (which is 6 inches less) is 9.
Length=15 inches
Width=9 inches
