Question

Mr Duma nendly inherited a rectangular plot, part of the estate len by his late father. The plot with the following dimensions: Length - 2r +1Width - - 1 S R He has plans to do the following projects on the plot: Project A: Purchase fencing material to enclose three sides of the plot as follows: SP. PQ and QR Project B: Build a fancy wall on the front side, SR. Project C: Construct paving for a third of the plot. 21 Determine the formulae that will be suitable for each of the projects mentioned above. For each formula, also give the reason for your choice. Write down the information in the table attached Project Formulae Reason 4. - B 2.x-1 С 3​

Answer 1

The given equations for the length and with can be used by Mr. Duma

to calculate the amount of materials required.

Response:

The completed table with responses is presented as follows;

$\begin{array}{|c|c|c|} \mathbf{Project} &\mathbf{Formulae}&\mathbf{Reason}\\A&4 \cdot x - 1&Length \ of \ fencing = SP + PQ +QR \\B&2 \cdot x + 1&Length \ of \ fancy \ wall = Length \ of \ SR \\C& \dfrac{1}{3} \times \left(2 \cdot x + 1\right) \times \left( x - 1 \right) &Area \ of \ paving = \frac{1}{3} \times Area \ of \ plot \end{array}$

How is the rectangular plat with dimensions given as equations (expressions) evaluated?

Given parameters are;

Length of the plot = 2·x + 1

Width of the plot = x - 1

Project A;

The length of the fencing is given by the sum of the lengths of the three

sides as follows;

SP = QR are width sides of the plot = x - 1

PQ is a longer or a length side of the plot = 2·x + 1

Total length of fencing = SP + PQ + QR

Which gives;

• Formula for the fencing project = 2·x + 1 + (x - 1) + (x - 1) = 4·x - 1

Project B;

• Formula for the length of the fancy wall = SR = PQ = 2·x + 1

Project C;

The area of the paving, $\mathbf{A_{paving}}$, which is one third of the area of the plot is therefore;

• $A_{paving} = \underline{ \dfrac{1}{3} \times \left(2 \cdot x + 1\right) \times \left( x - 1 \right)} = \dfrac{1}{3} \times \left(2 \cdot x^2 - x - 1 \right)$

The completed table of information for the project, formula and

reasons is presented as follows;

$\begin{array}{|c|c|c|}Project &Formulae&Reason\\A&4 \cdot x - 1&Length \ of \ fencing = SP + PQ +QR \\B&2 \cdot x + 1&Length \ of \ fancy \ wall = Length \ of \ SR \\C& \dfrac{1}{3} \times \left(2 \cdot x + 1\right) \times \left( x - 1 \right) &Area \ of \ paving = \frac{1}{3} \times Area \ of \ plot \end{array}$

Part of the question that appear missing based on a similar question posted online is presented as follows;

Area of a rectangle = Length × Width

Therefore;

Area of the plot = (2x + 1) × (x - 1) = 2·x² - x - 1

Learn more about working with variables here:

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https://brainly.com/question/92806