Question

Geometry math question

Answer 1

An isosceles triangle is one where two sides are equal to each other. The third side is of a different length.

At first glance, choice A looks like the answer because we have two sides that are the same length (the sides of length 1). However, this triangle is not possible because 1+1 = 2 which is less then 3. For a triangle to be possible, adding up two sides must be larger than the third side. I'm using the triangle inequality theorem here.

This works for choice D since 6+6 = 12 which is greater than 5. Also 5+6 = 11 which is greater than 6. So the answer is choice D

Answer 2

In an isosceles triangle, at least two sides must have the same length. Any triangle with 3 different side lengths must be eliminated. That leaves choices A and D.

Now we deal with A. 1, 1, 3.

Since 1 + 1 = 2, and that is less than 3, you cannot form a triangle with sides of lengths 1, 1, and 3, so A. is eliminated.

The answer must be D., and the lengths in D. do allow for a triangle.

Answer: D. {6, 6, 5}