Join Sarthaks eConnect Today - India's Largest Online Education Community!

A quadrilateralABCD with area2002 contains a point p insideABCD such that PA=24 PB=32 PC=28 PD=45find perimeter of ABCD

+3 votes
asked Aug 17, 2016 in Mathematics by Rahul Roy (7,895 points) 31 96 261

1 Answer

+2 votes
answered Aug 17, 2016 by vikash (21,277 points) 4 18 65
selected Sep 22, 2016 by sarthaks
Best answer

Let diagonals intersect at right angles. Then we have 

with equality if $P$ lies on $\overline{AC}$ and $\overline{BD}$ respectively. Thus

Since we have the equality case, $\overline{AC} \perp \overline{BD}$ at point $P$ 

By the Pythagorean Theorem,

The perimeter of $ABCD$ is 

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

One Thought Forever

“There is a close connection between getting up in the world and getting up in the morning.“
– Anon