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# Triangle ABC has two of its three sides as 9 units and 12 units respec

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DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1412
Location: India
Triangle ABC has two of its three sides as 9 units and 12 units respec  [#permalink]

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25 Jul 2018, 10:12
00:00

Difficulty:

55% (hard)

Question Stats:

22% (01:18) correct 78% (01:56) wrong based on 18 sessions

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Triangle ABC has two of its three sides as 9 units and 12 units respectively in length. Triangle PQR has one of its three sides as 12 units in length. Is the area of triangle ABC same as that of triangle PQR?

(1) Triangle ABC is an isosceles triangle with AB = AC in length.

(2) Triangle PQR is equilateral.
Math Expert
Joined: 02 Aug 2009
Posts: 7106
Re: Triangle ABC has two of its three sides as 9 units and 12 units respec  [#permalink]

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25 Jul 2018, 18:53
Triangle ABC has two of its three sides as 9 units and 12 units respectively in length. Triangle PQR has one of its three sides as 12 units in length. Is the area of triangle ABC same as that of triangle PQR?

(1) Triangle ABC is an isosceles triangle with AB = AC in length.
Triangle PQR can have other two sides 100 each... Area of PQR is more
Triangle PQR can have other two sides same as that of ABC... Area will be same
Insufficient

(2) Triangle PQR is equilateral.
This means all sides are equal so area =$$\frac{√3}{4}*12^2=√3*3*12=36√3$$
Max area of ABC is when it is a right angle triangle and the third side is the greatest or hypotenuse
So area =1/2 *9*12=54
35√3>54
So the area can never be equal
Sufficient

B
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Triangle ABC has two of its three sides as 9 units and 12 units respec &nbs [#permalink] 25 Jul 2018, 18:53
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