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PQRS is a quadrilateral whose diagonals are perpendicular

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PQRS is a quadrilateral whose diagonals are perpendicular [#permalink]

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New post 16 Dec 2017, 10:28
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PQRS is a quadrilateral whose diagonals are perpendicular to each other. If PQ=16 cm, QR=12 cm and RS=20 cm, what is the value of PS.
A) 8\(\sqrt{2}\)
B) 12\(\sqrt{2}\)
C) 16\(\sqrt{2}\)
D) 20\(\sqrt{2}\)
E) 24\(\sqrt{2}\)
[Reveal] Spoiler: OA

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PQRS is a quadrilateral whose diagonals are perpendicular [#permalink]

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New post 16 Dec 2017, 11:17
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souvonik2k wrote:
PQRS is a quadrilateral whose diagonals are perpendicular to each other. If PQ=16 cm, QR=12 cm and RS=20 cm, what is the value of PS.
A) 8\(\sqrt{2}\)
B) 12\(\sqrt{2}\)
C) 16\(\sqrt{2}\)
D) 20\(\sqrt{2}\)
E) 24\(\sqrt{2}\)


Let the Diagonals intersect at Point O.

\(OP^2 + OQ^2 = 16^2 ------------- Eqn 1\)
\(OQ^2 + OR^2 = 12^2 ------------- Eqn 2\)
\(OR ^2 + OS^2 = 20^2 ------------- Eqn 3\)

We have to find \(OP^2 + OS^2\)

\(Eqn 3 - Eqn 2 + Eqn 1 = 512\).. Which Means \(PS\)= \(16\sqrt{2}\)
PQRS is a quadrilateral whose diagonals are perpendicular   [#permalink] 16 Dec 2017, 11:17
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PQRS is a quadrilateral whose diagonals are perpendicular

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