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

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

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New post 17 Aug 2017, 23:39
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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
[Reveal] Spoiler: OA

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Re: Triangles ABC and ABD share side AB. Triangle ABC has area Q and [#permalink]

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New post 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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Triangles ABC and ABD share side AB. Triangle ABC has area Q and [#permalink]

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New post 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

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

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New post 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
tri.png [ 10.2 KiB | Viewed 311 times ]


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Re: Triangles ABC and ABD share side AB. Triangle ABC has area Q and [#permalink]

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New post 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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Re: Triangles ABC and ABD share side AB. Triangle ABC has area Q and   [#permalink] 18 Aug 2017, 05:41
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