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PQRS is a quadrilateral whose diagonals are perpendicular

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Senior Manager
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 432
Location: India
GPA: 3.64
PQRS is a quadrilateral whose diagonals are perpendicular [#permalink]

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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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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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