2. CBQ - Area and perimeterof the garden

Question:

4 m.

A square garden has a side length of \((x+4)\) \(meters\). The garden is being redesigned to maximize planting area within a fixed fencing budget. Garden planners want to analyze how changes in side length affect both the total area and the amount of fencing required to improve future layouts.

1. Write the polynomials representing the area of the garden.

\(x^{2}+4x+8\)
\(x^{2}+8x+16\)
\(x^{2}+4x+16\)
\(x^{2}+8x+8\)

2. If \(x=8\), what is the area of the garden?

\(144\) \(\text{square meters}\)
\(24\) \(\text{square meters}\)
\(48\) \(square\) \(meters\)
\(64\) \(\text{square meters}\)
\(36\) \(\text{square meters}\)

3. If the length is increased by \(2\) \(meters\), what is the new polynomial representing the area?

\(x^{2}+10x+36\)
\(x^{2}+12x+36\)
\(x^{2}+12x+25\)
\(x^{2}+10x+25\)

4. If the side length \((x+4)\), what is the perimeter of the garden?

\(x^{2}+16\)
\(x^{2}+8x+16\)
\(2x+8\)
\(4x+16\)

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