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Home » \sin 45^\circ = \frac{\sqrt2}2 - IX Labs

\sin 45^\circ = \frac{\sqrt2}2 - IX Labs

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 A square has an area of \(64\) square units. If each side length is increased by \(50\%\), what is the new area of the square?

📌 The area of the original square is \(64\) square units, so each side length \(s\) is:

📌 s = \sqrt{64} = 8 \text{ units}

📌 Increasing each side by \(50\%\) gives a new side length:

📌 s_{\text{new}} = 8 + 0.5 \times 8 = 1.5 \times 8 = 12 \text{ units}

📌 The new area is:

📌 A_{\text{new}} = (12)^2 = 144 \text{ square units}

📌 Alternatively, since area scales by the square of the side length factor (\(1.5^2 = 2.25\)):

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