Question

The distance between opposite corners of a rectangular field is four more than the width of the field .The length of the field is twice its width . Find the distance between the opposite corners. Round to the nearest tenth.

Short answer

The distance between the opposite corners is 8.

Step-by-step solution

Given information 

The given statement is the length of the field is twice its width.The distance between opposite corners of a rectangular field is four more than the width of the field.

The distance between the opposite corners

Take distance between corners is d.

Width is w and length is l.

$$\begin{gathered} d=4+w \\ l=2w \\ Bypythagorastheorem \\ {\left(2w\right)}^2+{\left(w\right)}^2={\left(4+w\right)}^2 \\ 4w^2+w^2=16+w^2+8w \\ 4w^2-8w-16=0 \\ Take4outasacommon \\ {w}^2-2w-8=0 \end{gathered}$$

Using quadratic equation

a =1 , b = -2 and c = -8

$$\begin{gathered} w=\frac{-\left(-2\right)\pm \sqrt{{\left(-2\right)}^2-4\left(1\right)\left(-8\right)}}{2} \\ w=\frac{2\pm \sqrt{4+32}}{2} \\ w=\frac{2\pm 6}{2} \\ w=4 \\ \mathrm{The}\mathrm{distance}\mathrm{between}\mathrm{the}\mathrm{opposite}\mathrm{corners}\mathrm{is}8. \end{gathered}$$