P is any point inside the rectangle ABCD. If PA = 27cm. PB = 21 cm. PC = 6 cm then the length PD (in cm) is equal

Correct option is B

Given:

P is any point in rectangle ABCD such that

PA = 27cm,PB = 21cm and PC = 6cm

Formula Used:

If P is any point inside a rectangle ABCD then

​$$PA^2 + PC^2 = PB^2 + PD^2$$​​

Solution:

​$$PD^2 = PA^2 +PC^2 - PB^2$$​​

$$PD^2 = (27)^2 +(6)^2-(21)^2$$​

​$$PD^2 = 729 +36 - 441 = 324$$​​

​$$PD = \sqrt{324} = 18cm$$​​