Let's solve the equation step by step:
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Evaluate the powers: \[ a^2 + 162 = 202 \quad \Rightarrow \quad a^2 + 162 = 400 \] (This is given in your problem, assuming it's the interpretation of your question, but we start from \(a^2 + 162 = 202\))
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Isolate the variable: \[ a^2 + 162 = 202 \quad \Rightarrow \quad a^2 = 202 - 162 \] \[ a^2 = 40 \]
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Take the square root of both sides: \[ a = \sqrt{40} \]
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The missing side length in simplified form: \[ a = \sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10} \] If you're looking for a numerical approximation, \[ a \approx 6.32 \quad (\text{or simply write } a = 6.32 \text{ if numerical output is needed like in other steps}) \]
Thus, the final answers are:
- For step 2, \( a^2 = 40 \)
- For step 4, \( a \) (the missing side length) is approximately \( 6.32 \) or \( 2\sqrt{10} \). If only a single numerical answer is satisfactory, \( 6.32 \) would be acceptable.