The plot

Mr. Duma recently inherited a rectangular plot, part of the estate left by his late father. The plot with the following dimensions: Length=2x+1; Width=x-1.
Determine the formula, in terms of x, that best describes the area of the rectangular plot.

He has plans to do the following projects on the plot (rectangle has corner PQRS):
Project A: Purchase fencing material to enclose three sides of the plot: SP, PQ, and QR.
Project B: build a fence wall on the front side, SR.
Project C: construct paving for a third of the plot.

Find the formula suitable for each of the following projects mentioned above. For each formula, give the reason for your choice. Determine the formula in terms of x that best describes the area of the plot.

Correct answer:

S = 2x^2-x-1
A = 4x-1
B = 2x+1
C = (2x^2-x-1)/3

Step-by-step explanation:

$$\begin{gathered} L=2x+1 \\ W=x-1 \\ S=L\cdot W \\ S=(2x+1)\cdot (x-1) \\ S=2x^2+x-2x-1 \\ S=2x^2-x-1 \end{gathered}$$

$$\begin{gathered} A=|SP|+|PQ|+|QR|=W+L+W \\ A=2W+L \\ A=2\cdot (x-1)+2x+1 \\ A=2x-2+2x+1 \\ A=4x-1 \end{gathered}$$

$$\begin{gathered} B=|SR|=L \\ B=2x+1 \end{gathered}$$

$$\begin{gathered} C=\frac{1}{3}\cdot S \\ C=(2x^2-x-1)/3 \end{gathered}$$

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