Malbash212 wrote:

soumya1989 wrote:

If x>0, and two sides of a certain triangle have lengths 2x+1 and 3x+4 respectively, which of the following could be the length of the third side of the triangle?Indicate

all possible lengths.

A) \(4x+5\)

B) \(x+2\)

C) \(6x+1\)

D) \(5x+6\)

E) \(2x+17\)

Are you sure answer E is ok?

Yes. Note that choice E is always bigger than 2x + 1. However, it is not always bigger than 3x + 4. When 2x + 17 and 2x + 1 are combined, though, they equal 4x + 18, which is always bigger than 3x + 4. This means that there are times when 3x + 4 is the hypotenuse, and the sum of both legs is greater than it.

For example, take x = 10. When that is the case, the triangle has side lengths 21, 27, and 34. This is totally fine, as the sum of the two smaller sides is greater than the length of the third side.