If the length of side AB is 17, is triangle ABC a right tria

Question

If the length of side AB is 17, is triangle ABC a right triangle?

(1) The length of side BC is 144.
(2) The length of side AC is 145.

Bunuel · Accepted Answer

If the length of side AB is 17, is triangle ABC a right triangle?

(1) The length of side BC is 144 --> there are infinitely many triangles possible with the sides of 17 and 144, two of them will be right triangles (17^2+144^2=x^2, where x is a hypotenuse and 17^2+y^2=144^2, where y is an another leg) and others will not. Not sufficient.

(2) The length of side AC is 145. Not sufficient for the same reason.

(1)+(2) We know all the sides hence, even without actual calculation, we can find out whether the triangle is right or not. Sufficient. (As a matter of fact it is a right triangle: 17^2+144^2=145^2)

Answer: C.

kys123 · Answer

Bunuel or anyone else can I ask a question. So if a triangle fits into the Pa Theorem then it has to be a right angle or could it fit the theorem n not be a right angle. Thanks

Bunuel · Answer

Yes, the reverse of Pythagorean theorem is also true:  for any triangle with sides a, b, and c, if a^2+b^2=c^2, then the angle between the sides a and b is 90 degrees .

dchow23 · Answer

(1) INSUFFICIENT: With only two sides of the triangle, it is impossible to determine whether a2 + b2 = c2.

(2) INSUFFICIENT: With only two sides of the triangle, it is impossible to determine whether a2 + b2 = c2.

(1) AND (2) SUFFICIENT: With all three side lengths, we can determine if a2 + b2 = c2. It turns out that 172 + 1442 = 1452, so this is a right triangle. However, even if it were not a right triangle, this formula would still be sufficient, so it is unnecessary to finish the calculation.

Sachin9 · Answer

Hi Experts, Do we really see such calculation intensive Questions on GMAT? :shock:

Regards, Sachin

Vips0000 · Answer

Actually there is no intensive calculation involved. The only calculation required here is to check - when combining statement 1 and 2, a triangle can be formed or not, that is sum of 2 lengths is greater than third or not. 
Once it is known that a triangle can be formed and you have lenght of each side, you have sufficient details to answer if it is a right angle or not. Data sufficiency question wants to know only that. you dont need to apply theorem to calculate it.

Sachin9 · Answer

I beg to differ.. 
Its already stated that it is a triangle, Our job is to check if its a right angled triangle..and to check that we need to apply the theorem of the great pythagorus and this application of theorem in my opinion is calculation intensive.

Regards,
Sachin

Bunuel · Answer

Please check the following post to see that no calculations are needed to solve the question: if-the-length-of-side-ab-is-17-is-triangle-abc-a-right-tria-127069.html#p1039631

Sachin9 · Answer

Oh yeah..

Its only a DS Question not a PS.

Thanks Bunuel..

chigiwigi · Answer

For such large calculations, how do you find out that it's a right triangle? Thanks.

Zinsch123 · Answer

Did you read the replies in this thread? The question is whether we have sufficient information to determine whether it is a right triangle. The question is NOT whether it is a right triangle.

We know all 3 sides of the triangle. Therefore, we have sufficient information to determine whether it is a right triangle. It is NOT necessary to actually calculate whether it indeed is one.

chigiwigi · Answer

Ya, makes sense, thanks again.

masoomjnegi · Answer

For a triangle to be isosceles triangle sides of the triangle must follow a2 + b2 = c2 where ‘c’ is the largest side of the triangle.
Statement 1. Here, we know the length of 2 sides but we are still unaware of the third side. So, we can use the above given equation. Hence, Insufficient.
Statement 2. We know the length of 2 sides of the triangle but we are unaware of the third side of the triangle. So, we can’t use the above equation. Hence, Insufficient.
Statement 1 & 2 together. Using the data given in the question statement and statement 1 and 2 together, we know all three sides of triangle. 
1442 + 172 = 20736 + 289 = 21025 = 1452. 
So, the triangle is a right triangle. Hence, Sufficient.

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If the length of side AB is 17, is triangle ABC a right tria

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GMAT Data Sufficiency (DS) Questions

If the length of side AB is 17, is triangle ABC a right tria

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