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# Triangles ABC and ABD share side AB. Triangle ABC has area Q and

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Math Expert
Joined: 02 Sep 2009
Posts: 55230
Triangles ABC and ABD share side AB. Triangle ABC has area Q and  [#permalink]

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17 Aug 2017, 23:39
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Difficulty:

75% (hard)

Question Stats:

38% (02:13) correct 62% (02:01) wrong based on 47 sessions

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Triangles ABC and ABD share side AB. Triangle ABC has area Q and triangle ABD has area R. If AD is longer than AC, and BD is longer than BC, which of the following could be true?

I. R > Q
II. R = Q
III. R < Q

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II and III

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Joined: 14 Sep 2016
Posts: 129
Re: Triangles ABC and ABD share side AB. Triangle ABC has area Q and  [#permalink]

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18 Aug 2017, 04:08
If we consider AB as the common base then in that R > Q since BD greater than BC and on the other hand AD is greater than AC that makes the height more for triangle ADB greater and in turn R > Q

Option A

Some other feedback on this one will be really helpful.
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Joined: 18 Aug 2016
Posts: 618
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Triangles ABC and ABD share side AB. Triangle ABC has area Q and  [#permalink]

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18 Aug 2017, 05:14
Bunuel wrote:
Triangles ABC and ABD share side AB. Triangle ABC has area Q and triangle ABD has area R. If AD is longer than AC, and BD is longer than BC, which of the following could be true?

I. R > Q
II. R = Q
III. R < Q

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II and III

if we consider angle ABC=ABD=90 (points C, B, D are on straight line) then by area formula we can say that R>Q as as BD >BC
if the rest two sides are greater than the respective sides of other triangle and third side is same. Always the area of the triangle with bigger sides will be higher than another.
ABC = sides are x,y,z ABD = sides are x,p,q (p>y and q>z)
Sc = (x+y+z)/2 and Sd = (x+p+q)/2
$$Ac = \sqrt{(Sc (Sc-x)(Sc-y)(Sc-z))}$$
$$Ad = \sqrt{(Sd (Sd-x)(Sd-p)(Sd-q))}$$
here
Sd>Sc
Sd-x>Sc-x
Sd-p>Sc-y
Sd-q>Sc-z
Hence irrespective of length of sides Area of ABD(R)>ABC(Q)

Please correct me if i am wrong
A
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Luckisnoexcuse
Math Expert
Joined: 02 Aug 2009
Posts: 7683
Triangles ABC and ABD share side AB. Triangle ABC has area Q and  [#permalink]

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18 Aug 2017, 05:34
Bunuel wrote:
Triangles ABC and ABD share side AB. Triangle ABC has area Q and triangle ABD has area R. If AD is longer than AC, and BD is longer than BC, which of the following could be true?

I. R > Q
II. R = Q
III. R < Q

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II and III

Hi,

good Q Bunuel

Luckisnoexcuse and kunalsinghNS , you both are restricting your triangle between the side AB..
refer the attached sketch..
Black coloured triangle - Area Q
Red coloured Q<R
Blue coloured Q>R
Brown coloured Q=R

so all possible
E
Attachments

tri.png [ 10.2 KiB | Viewed 884 times ]

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Joined: 29 Mar 2016
Posts: 6
Re: Triangles ABC and ABD share side AB. Triangle ABC has area Q and  [#permalink]

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18 Aug 2017, 05:41
E.

For R = Q, If you imagine dragging D downward, eventually the height (area of triangle ABD) will equal the height (area of triangle ABC), and then after that it will be bigger i.e R < Q
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Posts: 10980
Re: Triangles ABC and ABD share side AB. Triangle ABC has area Q and  [#permalink]

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08 May 2019, 06:51
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Re: Triangles ABC and ABD share side AB. Triangle ABC has area Q and   [#permalink] 08 May 2019, 06:51
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# Triangles ABC and ABD share side AB. Triangle ABC has area Q and

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