# Isosceles Triangle Geometry Problem

Bashyboy

## Homework Statement

The measure of the sides of an isosceles triangle are represented by x + 5, 3x +13, and 4x + 11. What are the measures of the sides? Two answers are possible.

## The Attempt at a Solution

Well, I set up three different triangles, to account for the different placements of the sides; but I only came up with one solution. Where is the second solution coming from?

## Answers and Replies

Homework Helper
Two of those sides must be equal, right? Pick two of them, set them equal and find x. There are actually three different ways to do that. You'll find one value of x doesn't work.

Bashyboy
Well, I did do that, and I got -8, -6, and 2.

Homework Helper
Well, I did do that, and I got -8, -6, and 2.

Are those the x values? How did you get -8 and -6? I did get x=2 for one pair.

Bashyboy
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.

Homework Helper
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.

And which one of those gave you x=(-3)? I'm ok with x=2 and x=(-4).

Bashyboy
Blimey, I erred once again; the -3 should be a -2, and I found it by setting x + 5 = 4x + 11

Homework Helper
Blimey, I erred once again; the -3 should be a -2, and I found it by setting x + 5 = 4x + 11

Ok, so you've got x=2, -2 or -4. Which of those correspond to real triangles? Check what the side lengths are in each case.

Bashyboy
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?