Question

If the area of the rectangle is 4836 square feet find the length of the rectangle

Answer 1

- Let the length of the rectangle be x

- Let the width of the rectangle be y.

- Thus, we can interpret the lines of the question as follows:

`\begin{gathered} \text{ The length is 30 less than 6 times the width can be written as} \\ x=6y-30\text{ (Equation 1)} \\ \\ \text{The area of the rectangle is 4836. This is written as:} \\ xy=4836\text{ (Equation 2)} \end{gathered}`

- Now, let us solve these two equations simultaneously.

- We shall proceed by solving the system of equations graphically.

- Wherever the graphs of Equation 1 and Equation 2 intersect represents the solution to the system of equations

- The plot of the equations is given below

- Observe that the graphs cross at two points. The first point is positive and the other, negative.

- Since we cannot have negative lengths (x) or width (y), we can discard the negative coordinates.

- Thus, the length (x) and width (y) are given below:

`\begin{gathered} \text{length(x)}=156 \\ \text{width(y)}=31 \end{gathered}`

Final Answer

The length of the rectangle is 156 feet