In the figure above, what is the area of triangle ABC ?

Question

https://gmatclub.com/forum/download/file.php?id=45113 In the figure above, what is the area of triangle ABC ? (1) The length of BC is 13. (2) y = 90 2018-11-15_1503.png

DavidTutorexamPAL · Answer

Hopefully, we recognize that 5,12 are part of the Pythagorean triplet 5,12,13, in which case we'll look for this triplet in our answers.

(1) tells us that the third side is in fact 13 in which case the triangle must be right angle and the area is 5*12/2 = 30
(2) gives the same information as (1).

(D) is our answer.

Archit3110 · Answer

For such questions in geometry where in details are not clearly given we should not assume values ..
stmnt 1: sufficient, triplet phythogerous
smtn 2+ sufficient

option D

EgmatQuantExpert · Answer

Given:  
 • A triangle ABC
o AC = 12
o AB = 5
o Angle BAC = y degrees

To find:  
 • The area of triangle ABC

Analysing Statement 1  
 • BC = 13
Now, if we observe,  BC^2 = AB^2 + AC^2 
•  13^2 = 12^2 + 5^2 
• Implies, ABC is a right-angled triangle with y = 90 degrees
• Thus, area of ABC =  \frac{1}{2} * 12 * 5 = 30

Therefore, Statement 1 is sufficient

Analysing Statement 2  
 • y = 90 degrees
• Thus, area of ABC =  \frac{1}{2} * 12 * 5 = 30

Therefore, Statement 2 is sufficient

Hence, the correct answer is Option D

Answer: D

https://e-gmat.com/blogs/wp-content/uploads/2016/12/Geometry-Ability-Quiz-4-e1480581478957.png

mba757 · Answer

Bunuel

How can we definitively state that the triangle is a right triangle? Is there any way that the triangle could not be a right triangle but have the Pythagorean triple numbers? (i.e., cannot it be a scalene triangle or some other triangle in which it's not a right triangle but has the triplet numbers?) I came across a similar problem today, and I thought it was possible

Bunuel · Answer

No. The reverse of a Pythagorean theorem is also true: if the lengths of the sides of a triangle are a, b, and c, and a^2 + b^2 = c^2, then we have a right triangle.

Also, if the lengths of the sides of a triangle are a, b, and c, where the largest side is c, then:

For a right triangle:  a^2 +b^2= c^2 .
For an acute (a triangle that has all angles less than 90°) triangle:  a^2 +b^2>c^2 .
For an obtuse (a triangle that has an angle greater than 90°) triangle:  a^2 +b^2<c^2 .

mba757 · Answer

Thank you  Bunuel

One last clarifying (  hypothetical  ) question: if the picture was "5" for one of the given sides and " 11 " for the other given side (and all else equal within the problem/statements), statement one would not be sufficient - correct? (and also be an obtuse triangle)

And therefore, given the above, only statement 2 would then be sufficient?

Bunuel · Answer

Knowing the lengths of all three sides if a triangle is enough to calculate its area (for example, with the help oh Heron's formula, which you don't need to memorize for the GMAT). So, no, the answer would still be D.

In the figure above, what is the area of triangle ABC ?

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