The problem involves finding the measures of the sides of an isosceles triangle represented by the expressions x + 5, 3x + 13, and 4x + 11. The original poster attempts to determine the possible values of x that satisfy the condition of an isosceles triangle.
Participants are actively engaging with the problem, sharing their calculations and questioning the validity of their results. There is recognition of the need to check the side lengths derived from the values of x to determine which correspond to valid triangles.
Some participants express confusion regarding negative values for side lengths and the implications for the triangle's validity. The discussion reflects on the necessity of ensuring all side lengths are positive to form a legitimate triangle.
Bashyboy said:Well, I did do that, and I got -8, -6, and 2.
Bashyboy said:Oh! terribly sorry: I meant to write -4 and -3. And I found them by creating three different triangles, each case having its side equal to on of the others. For instance, I said a = x + 5,
b = 3x + 13, and c = 4x + 11; then I arbitrarily assigned a and b to be the equivalent sides and set them equal to each other and solved for x. Then, in the second case, I said a = x + 5, but this time I set b = 4x + 11; and once again, I said that a and b were the sides of the isosceles triangle that were equal and consequently set them equal to each other and solved for x. I followed the same procedure for the third case.
Bashyboy said:Blimey, I erred once again; the -3 should be a -2, and I found it by setting x + 5 = 4x + 11
Bashyboy said:Oh, okay, I see: I never plugged the values back into each expression; as soon as I saw the negative value, I completely dismissed it, thinking that you can't have a negative measurement. So, the two answers should be 2 and -2? and this corresponds to two possible triangles?