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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 16, 2016 in Mathematics by Rahul Roy (7,955 points)

1 Answer

+2 votes
answered Aug 16, 2016 by vikash (21,287 points)
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