Question

ACTIVITY 2 (19) 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. Q a P SO 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. 2.1 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. Reason Project Formulae A B С (9)​

Answer 1

The sum of the lengths of three sides of the rectangle, gives the length

of the fencing, while one third of the rectangle area is for the pavement.

Responses:

Project A: The formula for the length of the fencing is, L = 4·x - 1

Project B: Length of the fancy wall = 2·x + 1

$Project \ C:Area \ of \ the \ paving = \underline{ \dfrac{2\cdot x^2 }{3} - \dfrac{x }{3} - \dfrac{1}{3}}$

Which method can be used to find the length and area of paving from the given equations?

Project A: Let QP and SR represent the longest sides of the rectangle, we have;

PQ = SR = 2·x + 1

Given parameters are;

Length of the rectangular plot = 2·x + 1

Width of the rectangular plot = x - 1

Vertices of the rectangular plot are; QPSR

Project A: Let QP and SR represent the longest sides of the rectangle, we have;

PQ = SR = 2·x + 1

Which gives;

SP = QR = x - 1

The length of the fencing, L = SP + PQ + QR = x - 1 + 2·x + 1 + x - 1 = 4·x - 1

• The formula for the length of the fencing is, L = 4·x - 1

Project B: The front side is SR

Therefore;

• Length of the fancy wall = 2·x + 1

Project C:

Area, A = Length × Width

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

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

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