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


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


Gravatar Chris Lele, Magoosh Tutor

Sep 27, 2012 • Comment

dash sha

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

May 16, 2014

Lucas Fink, Magoosh Tutor

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.

May 22, 2014

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