Two sides of an isosceles triangle have lengths of 3 and 10. Find the length of the third side.

If you think about a scale drawing... You can't have two lengths of THREE because the base would be much much shorter then 10. So what is your next option?

It is possible but it’s not 6 :/

Well, an isosceles triangle is like a regular triangle but with a fancy hat on top. Now, in an isosceles triangle, the two sides with equal lengths are called legs, and the third side is called the base. In this case, we know that the lengths of the legs are 3 and 10. So, if we have a triangle with legs of 3 and 10, I would say that the third side is just out for a coffee break and needs to be chased down with a tape measure. In other words, we don't have enough information to determine the length of the third side. Silly triangle, always keeping us on our toes!

To find the length of the third side of an isosceles triangle, we need to know the lengths of the two equal sides. In this case, we know that two sides have lengths of 3 and 10.

Since it is an isosceles triangle, two sides are equal. Let's call the length of the third side x.

We have two cases to consider:

1. The two equal sides are the lengths 3 and 3. In this case, the third side must also have a length of 3 because all three sides are equal.

2. The two equal sides are the lengths 10 and 10. In this case, the third side could be any length greater than 0 but less than 20 (the sum of the other two sides). Since triangles are commonly defined to have positive lengths, we can exclude any negative values for x, which leaves us with 0 < x < 20.

So, the length of the third side of the isosceles triangle can either be 3 if the two equal sides are both 3, or any value between 0 and 20 (exclusive) if the two equal sides are both 10.

12