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P is any point inside the rectangle ABCD. If PA = 87 cm, PB = 12 cm and PC = 96 cm, then the length of PD (in cm) is equal to:
Question

P is any point inside the rectangle ABCD. If PA = 87 cm, PB = 12 cm and PC = 96 cm, then the length of PD (in cm) is equal to:

A.

124

B.

126

C.

129

D.

130

Correct option is C

Given
Point P is inside rectangle ABCD
PA = 87 cm
PB = 12 cm
PC = 96 cm
Formula Used
PA2+PC2=PB2+PD2PA^2 + PC^2 = PB^2 + PD^2​​
Solution
Substitute the given values into the formula:
872+962=122+PD27569+9216=144+PD216785=144+PD2PD2=16785144PD2=16641PD=16641=12987^2 + 96^2 = 12^2 + PD^2 \\7569 + 9216 = 144 + PD^2\\16785 = 144 + PD^2\\PD^2 = 16785 - 144\\PD^2 = 16641\\PD = \sqrt{16641} = 129\\cm
Final Answer
So the correct answer is (c)

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