Question

A rectangular tablecloth has an area of 80 square feet . The width is 5 feet shorter than the length .what are the length and width of the tablecloth. Round to the nearest tenth of a foot.

Short answer

Therefore,the length and width of the tablecloth is 11.78 feet and 6.78 feet respectively.

Step-by-step solution

Given information

The given statement is the width is 5 feet shorter than the length .

Area is 80 square feet.

Area of a rectangle 

$$\begin{gathered} w=l-5 \\ A=80 \\ Areaofarec\tan gle=l\times w \\ 80=\left(l\right)\left(l-5\right) \\ 80=l^2-5l \\ {l}^2-5l-80=0 \end{gathered}$$

Using quadratic formula

$$\begin{gathered} l^2-5l-80=0 \\ a=1,b=-5andc=-80 \\ l=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ l=\frac{-\left(-5\right)\pm \sqrt{{\left(-5\right)}^2-4\left(1\right)\left(-80\right)}}{2} \\ l=\frac{5\pm \sqrt{345}}{2} \\ l=\frac{5\pm 18.57}{2} \\ l=\frac{23.75}{2} \\ l=11.78feet \\ w=11.78-5 \\ w=6.78feet \end{gathered}$$