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ABCD is a rectangle in which $A B = 10 c m, B C = 8 c m$ . A point P is taken on AB such that $P A = x$ , then the minimum value of $P C^{2} + P D^{2}$ is equal to

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150

168

178

answer is D.

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Detailed Solution

$P C^{2} + P D^{2} = {(10 - x)}^{2} + 64 + 64 + x^{2}$

$f (x) = {(10 - x)}^{2} + 128 + x^{2} f^{1} (x) = - 2 (10 - x) + 2 x x = 5 m i n . v a l u e = 25 + 128 + 25 = 178$

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