Source: Revised GRE PDF 2nd Ed. Section 5; #24 (p. 82)

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# In triangle ABC, the measure of angle B

Select All The Answer Choices That Apply In triangle ABC, the measure of angle B is 90°, the length of side AB is 4, and the length of side BC is x. If the length of hypotenuse AC is between 4 and 8, which of the following could be the value of x ? Indicate all such values. 1, 2, 3, 4, 5, 6

### 1 Explanation

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Chris Lele

Sep 27, 2012 • Comment

dash sha

Can i use the triangle theorem of the sum of two sides is greater than the 3rd one.?

Lucas Fink

The triangle theorem doesn't help us much. If we want to find the maximum length of BC, we would make AC its maximum length, too. That is, according to the question, 8. So then, the triangle theorem tells us that BC is less than 12. All of the answer choices are much lower than 12. Why is that?

Here's the important part: it MUST be a right triangle. The triangle inequality theorem is about ANY triangle. A triangle with sides of 4, 8, and 11.9 would not be a right triangle.

So that restriction (it being a right triangle) might make different limits. Maybe it must be less than 6, for example. That turns out not to be true, but we need to experiment to find that out.

Robert Paul

On a similar problem, after using your method, shouldn't we do a double check using the triangle inequality theorem?

Niloufar Hafizi, Magoosh Tutor

Hi Robert,
It's always helpful to double check - if we have the time. We could on this one, and we would see for all of those values that the triangle inequality theorem holds. It would be time-consuming though, to check for each set of two sides for all three values of x.

Since we have a right triangle here and used the Pythagorean Theorem, we can be pretty sure that the answer will follow the inequality theorem. If you would like to check I would check for the maximum and minimum values of x, 6 and 1.