$(72)^{2} + (61)^{2} = (199)^{2} - (?)^{2} - 420$

165

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198

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182

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171

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None of these

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Solution

The correct option is E None of these
Here, we can write it as
$?^{2} + 420 = (199)^{2} - {(72)^{2} + (61)^{2}} ?^{2} + 420 = 39601 - {5184 + 3721} ?^{2} + 420 = 39601 - {8905} ?^{2} + 420 = 30696 ?^{2} = 30696 - 420 ?^{2} = 30276 ? = \sqrt{30246} = 174$

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