In the given figure, ABCD is a square whose side is 4 cm. P is a point on the side AD. What is the minimum value (in cm) of BP + CP?

In the given figure, ABCD is a square whose side is 4 cm. P is a point on the side AD. What is the minimum value (in cm) of BP + CP?

Answer: Option A

Solution

Answer: Option A

Solution:

Let P is the mid point of AD
$$\begin{array}{rl}& BP=\sqrt{A{P}^2+A{B}^2}\\ & =\sqrt{A{P}^2+16}\\ & =\sqrt{2^2+16}\\ & =\sqrt{20}\\ & \text{Similarly }CP=\sqrt{20}\\ & BP+CP=\sqrt{20}+\sqrt{20}=4\sqrt{5}\end{array}$$