What is area of triangle ABC?

The answer is straight E. There are infinitely many right triangle with hypotenuse of 5 having different areas.

Hi Brunel,

Can you throw some light on how is that possible.
If hypotenuse is 5 then other two sides needs to be 3 and 4 .
so that would give us the area.

Let me ask you how do you know that the sides are 3 and 4? Are we told that the lengths of the sides must be integers? Does x^2 + y^2 = 5^2 have only one solution?

Hi kanigmat011,

While the 3/4/5 right triangle is a common enough right triangle in the realm of standardized testing (and you'll likely see it -or a multiple of it - at least once on Test Day), if you have just one side of a right triangle, then you have NO WAY of knowing what the other two sides are.

As a question places more and more 'restrictions' into play, then those 'restrictions' might help you to narrow the possibilities down to just one option, but without restrictions, you have to consider more than just the obvious options.

For example:
We're given a right triangle with a hypotenuse of 5 and no other restrictions. Using the Pythagorean Theorem, we have A^2 + B^2 = 5^2. It's POSSIBLE that the other two sides are 3 and 4, but those sides could just as easily be 1 and (root24).

With this same situation, if the prompt included the restriction that the missing sides were both INTEGERS, then the sides would have to be 3 and 4.

Here's another example:
If you have a right triangle and you know that two of the sides are 3 and 4, does the third side have to be 5?....

GMAT assassins aren't born, they're made,
Rich

Thanks a lot Rich that really helped

Rich,

I believe the answer to this Q is Yes.... The diagonal has to be '5' applying Pythagoras Theorem..........

Kindly clarify..

Thanks,
A

It is always good to learn the correct terms. It is the 'hypotenuse' in a right angled triangle and NOT a 'diagonal'.

The answer to Rich's question is NOT necessarily = 5. You are not told that the 2 sides making the right angle are 3 and 4. What if the hypotenuse of this right triangle = 4 and one of the other sides = 3. Then the 3rd side MUST be = \(\sqrt {7}\)

Hope this helps.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is area of triangle ABC?

A. AC=5
B. Angle ABC=90


In the original condition, for the triangle, there are 3 variables, which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer.
When 1) & 2), you cannot figure out the length of AB and area is not unique, which is not sufficient. Therefore, the answer is E.


-> For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

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