Question

The length of a rectangle is 11 m more than twice the width, and the area of the rectangle is 63m^2. Find the dimensions of the rectangleLength= mWidth= m

Answer 1

Length = 18 m

Width= 3.5 m

Explanation:

We have the following information:

`\begin{gathered} L=11+2x \\ W=x \\ A=L\cdot W=63 \end{gathered}`

We replace and calculate the value of x, in order to calculate the length and width:

`\begin{gathered} 63=x\cdot(11+2x) \\ 63=11x+2x^2 \\ 2x^2+11x-63=0 \\ \text{ we factor} \\ (2x-7)\cdot(x+9)=0 \\ 2x-7=0\rightarrow x=(7)/(2) \\ x+9=0\rightarrow x=-9 \end{gathered}`

Now, we replace the value of x:

`\begin{gathered} W=(7)/(2)=3.5 \\ L=11+2\cdot(7)/(2)=11+7=18 \end{gathered}`

So the length is 18 meters and the width is 3.5 meters