GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Aug 2019, 07:39

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# PQRS is a quadrilateral whose diagonals are perpendicular

Author Message
TAGS:

### Hide Tags

Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 1036
Location: India
GPA: 3.64

### Show Tags

16 Dec 2017, 11:28
2
2
00:00

Difficulty:

65% (hard)

Question Stats:

59% (02:34) correct 41% (01:46) wrong based on 29 sessions

### HideShow timer Statistics

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$$\sqrt{2}$$

_________________
Please give kudos, if you like my post

When the going gets tough, the tough gets going...
Director
Joined: 31 Jul 2017
Posts: 514
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)

### Show Tags

16 Dec 2017, 12:17
1
1
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 $$PS$$= $$16\sqrt{2}$$
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!
PQRS is a quadrilateral whose diagonals are perpendicular   [#permalink] 16 Dec 2017, 12:17
Display posts from previous: Sort by