If the lengths of two sides of an isosceles triangle are 4 and 9, what is the perimeter of the triangle?
This one is a little tricky. We know that in an isosceles triangle two sides are equal, so if we have given side lengths of 4 and 9 the remaining side is either 4 or 9. But which one?
The Triangle Inequality comes into play. This says any side of any triangle must be less than the sum of the other two sides. If our isosceles triangle has two sides of length 4, the third side can't be as long as 9!
So our isosceles triangle has sides of 4, 9, 9 rather than 4, 4, 9. The perimeter given in the answer follows.