Question

Two sides of an isosceles triangle measure 3 inches and 13 inches respectively. Find the length of the third side. Explain your reasoning.

Answer 1

An isosceles triangle is a triangle that has two sides of equal length. If the lengths of two sides of this isosceles triangle are 3 inches and 13 inches, then the third side would be a length of 13 inches.
This can be reasoned in that a base of 13 inches is too wide for two sides of 3 inches to meet and create a triangle, but a base of 3 inches would make a base small enough for two sides of 13 inches to meet and form an isosceles triangle.

Answer 2

Because the triangle is isosceles, two sides have the same length.

So, the triangle may have sides 3, 3, 13 OR 3, 13, 13

The triangle inequality theorem states that one side of a triangle is less than the sum of the other two.

3, 3, 13 cannot be the sides of any triangle because 13 is not less than 3 + 3 which is 6.

3, 13, 13 are the lengths of the triangle with 13 being the length of the third side.