- In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
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\caption{Figure 1}
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Figure 1 shows the plan view of a flower bed.
The flowerbed is in the shape of a triangle \(A B C\) with
- \(A B = p\) metres
- \(A C = q\) metres
- \(B C = 2 \sqrt { 2 }\) metres
- angle \(B A C = 60 ^ { \circ }\)
- Show that
$$p ^ { 2 } + q ^ { 2 } - p q = 8$$
Given that side \(A C\) is 2 metres longer than side \(A B\), use algebra to find
- the exact value of \(p\),
- the exact value of \(q\).
Using the answers to part (b),
calculate the exact area of the flower bed.