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Home » Find the area of the entire tiled rectangle: 16 * 11 = 176 square meters. - AMAZONAWS

Find the area of the entire tiled rectangle: 16 * 11 = 176 square meters. - AMAZONAWS

📅 March 6, 2026 👤 scraface
Mar 06, 2026
Find the area of the entire tiled rectangle: 16 * 11 = 176 square meters.

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📌 Solution: Complete the square for $x$ and $y$. For $x$: $9(x^2 - 2x) = 9[(x - 1)^2 - 1] = 9(x - 1)^2 - 9$. For $y$: $-16(y^2 - 4y) = -16[(y - 2)^2 - 4] = -16(y - 2)^2 + 64$. Substitute back: $9(x - 1)^2 - 9 - 16(y - 2)^2 + 64 = 144$. Simplify: $9(x - 1)^2 - 16(y - 2)^2 = 89$. The center is at $(1, 2)$. Thus, the center is $oxed{(1, 2)}$.
📌 The area is \( w imes (w + 4) = 7 imes 11 = 77 \) square meters.
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