Question

Let P be a point inside a rectangle ABCD. If PA = 3cm, PB = 4 cm and PC = 5 cm, find PD

• A. $3\sqrt{2}$ cm
• B. $5\sqrt{2}$ cm
• C. 12 cm
• D. 13 cm

Answer 1

Answer: (A)

$3\sqrt{2}$ cm

Given P be a point inside a rectangle ABCD. If PA = 3 cm, PB = 4 cm and PC = 5
Then $P{A}^2+P{C}^2=P{B}^2+P{D}^2$
Or $P{D}^2=P{A}^2+P{C}^2-P{B}^2$
SO $P{D}^2=(3{)}^2+(5{)}^2-\left(4^2\right)=9+25-16=18$
OR PD=$3\sqrt{2}$cm