General pythogrean Q

Question

If in a DS geometry Q a triangle that looks like a Right triangle but does not show the 90 deg symbol

and its legs are 8 and 6 is it still a Right Triangle ?

maanavrelan4gmat · Answer

Not necessarily.
 Sides in conjunction with Pythagorean theorem is a necessary but not sufficient condition for a triangle to be Right angled triangle.

What this implies is that, if the sides of a triangle are 6,8 and 10, they are a Pythagorean triplet but alone cannot guarantee that triangle to be right angled triangle.

Hope it will help.

koushikc · Answer

Vice versa of the pythogeran theorem may not be true. You cannot simply assume that in GMAT.
It might be just another trick played in the Q.

Bunuel · Answer

That's not correct.

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.

But this is not our case. If the sides of a triangle are 6 and 8, then the length of the third side can be any number from the following range: (8-6) 2<x<14 ( the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides ).

Now, if the length of the third side is say 10, then we would have a right triangle with sides 6, 8, and 10. But if the length of the third side is say 3, then we won't have a right triangle.

Notice that we also could have a right triangle if the length of the third side is  2\sqrt{7} :  (2\sqrt{7})^2+6^2=8^2 (in this case the side with the length of 8 will be hypotenuse).

Hope it's clear.

General pythogrean Q

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