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Triangle : gmat prep

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by kstv » Thu Apr 08, 2010 9:29 am
[email protected] wrote:easier way
consider RX is perpendicular on x-axis
then
OQRX a trapezoid, and
areaPQR=area (OQRX)-area(OPQ)-area(RPX)
=(OQ+RX)/2*OX - 1/2 *OP*OQ - 1/2 * PX* RX
=(3+4)/2*7 - 1/2 * 4*3 - 1/2 *3*4=24.5 - 6 - 6 =12. 5
good one in fact if you drop a perpendicular to y axis you get a rectangle.
The advantage is that u do not need to remember complicated formula.
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by outreach » Thu Apr 08, 2010 10:54 am
Area of isosceles trainge given by c/4*sqroot of (4a^2-c^2)
a is the length of isoceles side

section formula dist b/n point(x1,y1) and( x2,y2) is
dist=sqrt[(x1-x2)^2+(y1-y2)^2]

PQ=PR=5=a
QR=5sqroot of2=c



substituting in the formulae
5sqroot of2/4*sqroot of (4*5^2-(5sqroot of2)^2)
solving we get 12.5 as the answer
bhumika.k.shah wrote:Shorter and quicker way?
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by sanju09 » Thu Dec 31, 2015 10:54 pm
bhumika.k.shah wrote:Shorter and quicker way?
If we drop RS perpendicular to x-axis to meet x-axis in S, then OQRS is a trapezoid, whose area is ½ (3 + 4) (7) = 24.5; and the required area is obtained by chopping right triangles POQ and PSR out of 24.5 (see figure).

Area POQ = ½ (4)(3) = 6, and Area PSR = ½ (4)(3) = 6, added 12, subtracted from 24.5, we get area of triangle PQR = [spoiler]12.5.

Pick A[/spoiler]
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by GMATGuruNY » Thu Dec 31, 2015 11:28 pm
In the rectangular coordinate system below, the are of triangular region PQR is

Image

12.5
14
10srt2
16
25
Image

The area of the rectangle drawn around triangle PQR = 7*4 = 28.
Since triangle PQR takes up less than half the rectangle, PQR < 14.

The correct answer is A.
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by [email protected] » Fri Jan 01, 2016 9:59 am
Hi All,

There's a great tactic that's worth remembering on graphing questions: any diagonal line on a graph is part of a right triangle (that you can draw and use to figure out the length of the line). That tactic works perfectly on this prompt (as you can see from Mitch's explanation). You'd be surprised how often that one "math move" can be used to help you solve graphing questions, so keep it in mind as you continue to study.

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by Brent@GMATPrepNow » Fri Jan 01, 2016 10:55 am
Image
Let's draw a rectangle around the triangle (as shown below) and then subtract from the rectangle's area (28), the areas of the 3 right triangles that surround the triangle in question.

We get the following:
Image

So, the area of PQR = 28 - (3.5 + 6 + 6) = 12.5

Answer = A

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