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

Question

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

kunalsinghNS · Answer

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.

Luckisnoexcuse · Answer

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

chetan2u · Answer

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

shukla880 · Answer

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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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

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