Last visit was: 25 May 2024, 10:36 It is currently 25 May 2024, 10:36

Close

GRE Prep 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
Your Progress

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

Practice
Pays

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Intern
Intern
Joined: 03 Jun 2020
Posts: 14
Own Kudos [?]: 7 [1]
Given Kudos: 8
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 28812
Own Kudos [?]: 33400 [1]
Given Kudos: 25278
Send PM
avatar
Intern
Intern
Joined: 26 Jul 2020
Posts: 2
Own Kudos [?]: 2 [1]
Given Kudos: 0
Send PM
avatar
Intern
Intern
Joined: 19 Aug 2022
Posts: 1
Own Kudos [?]: 1 [1]
Given Kudos: 0
Send PM
Re: In a right triangle PQR, X and Y are mid points of PQ and PR [#permalink]
1
Area of PXTY is not 15 as multiplying adjacent sides to find area only works for rectangles and squares and PXTY is neither.

heres how I did it. pls correct me if I'm wrong.

we have PX = XQ = 3, PY= YR = 5 ( not explaining this since other users have explained already)

now area of PQR = 1/2 * BASE * HEIGHT = 6*8/2 = 24.
and area of PXTY = area of ▲PQR - (Area of ▲XQT + Area of ▲YTR)

consider QT = x , then TR = 8-x.

then area of ▲XQT = 1/2 * 3 * x = 3x/2 (since this is a rt. triangle length of perpendicular = height)

however ▲YTR is not right angled, so we draw a line from Y that intersects QR perpendicularly at point Z.
Now midpoint theorem states that XY || QR. since YZ is perpendicular to QR, it must also perpendicular to XY. So all angles of quadrilateral XYZQ are 90° thus XYZQ is a square. hence XQ = YZ = 3.
So area of ▲YTR = 1/2 * TR * YZ = 1/2 * (8-x) * 3 = 12 - (3x/2).

Now add area of ▲XQT + ▲YTR = [3x/2] + [12 - (3x/2)] = 12.

Area of PXTY = Area of ▲PQR - (Area of ▲XQT + ▲YTR)
= 24 - 12
= 12.

Option C is the correct answer.
avatar
Intern
Intern
Joined: 24 Oct 2022
Posts: 1
Own Kudos [?]: 1 [1]
Given Kudos: 0
Send PM
In a right triangle PQR, X and Y are mid points of PQ and PR [#permalink]
1
It is a very easy question if you know the property that the median of a triangle divides the triangle into 2 equal halves.
As Line TX is the median, triangle PTQ have two equal area triangles: PXT and QXT.
Similarly, triangle PRT is divided into two equal are triangles: PTY and TRY.

In this way we get area of full triangle, PQR = 1/2 * PXTY

We know area of PQR = 1/2*base*height = 1/2*6*8= 24.
so PXTY = 1/2*24=12

Attachment:
GRE triangle (10).jpg
GRE triangle (10).jpg [ 77.49 KiB | Viewed 563 times ]


So the correct answer is C.
Intern
Intern
Joined: 04 Jan 2023
Posts: 8
Own Kudos [?]: 0 [0]
Given Kudos: 64
Send PM
Re: In a right triangle PQR, X and Y are mid points of PQ and PR [#permalink]
Carcass how do we tell the quadrilateral is a rectangle?
Verbal Expert
Joined: 18 Apr 2015
Posts: 28812
Own Kudos [?]: 33400 [0]
Given Kudos: 25278
Send PM
Re: In a right triangle PQR, X and Y are mid points of PQ and PR [#permalink]
Expert Reply
Sorry, where you saw we are dealing with a rectangle ?
Intern
Intern
Joined: 04 Jan 2023
Posts: 8
Own Kudos [?]: 0 [0]
Given Kudos: 64
Send PM
Re: In a right triangle PQR, X and Y are mid points of PQ and PR [#permalink]
Carcass wrote:
PQ=6 and QR = 8
AND

PR = 10

PX is = 3 and PY=5

You know these two sides. \(3 \times 5 = 15\) regardless you do not know where is T. Actually is it a rectangle.

Regards


Carcass how do we tell PXTY is a rectangle?
Verbal Expert
Joined: 18 Apr 2015
Posts: 28812
Own Kudos [?]: 33400 [0]
Given Kudos: 25278
Send PM
Re: In a right triangle PQR, X and Y are mid points of PQ and PR [#permalink]
Expert Reply
Attachment:
GRE triangle.jpg
GRE triangle.jpg [ 2.31 MiB | Viewed 479 times ]
Manager
Manager
Joined: 16 Dec 2019
Posts: 190
Own Kudos [?]: 122 [1]
Given Kudos: 59
Send PM
In a right triangle PQR, X and Y are mid points of PQ and PR [#permalink]
1
Another solution using Ratios

Area of PXTY = Area of PQR - (Area of XQT + Area of YTR)
= 24 - (24 * 3/6 * QT/QR + 24 * 5/10 * TR/QR)
= 24 - 12( QT + TR )/QR
= 12

Option C
Prep Club for GRE Bot
[#permalink]
   1   2 
Moderators:
Moderator
1085 posts
GRE Instructor
218 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne