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:

Correct option is C

Given
Point P is inside rectangle ABCD
PA = 87 cm
PB = 12 cm
PC = 96 cm
Formula Used
​$$PA^2 + PC^2 = PB^2 + PD^2$$​​
Solution
Substitute the given values into the formula:
$$87^2 + 96^2 = 12^2 + PD^2 \\7569 + 9216 = 144 + PD^2\\16785 = 144 + PD^2\\PD^2 = 16785 - 144\\PD^2 = 16641\\PD = \sqrt{16641} = 129\\$$cm
Final Answer
So the correct answer is (c)