Question

An isosceles triangle has legs with length 11 units. Which of the following could be the perimeter of the triangle? Choose all that apply. Explain your reasoning.

a. 22 units
b. 24 units
c. 34 units
d. 43 units
e. 44 units

Answer 1

Let's deduce the base length for each option. Since the two legs are 11 units long, they sum to 22 units. The remaining units will be the base length:

• 22 units -> base length 0
• 24 units -> base length 2
• 34 units -> base length 12
• 43 units -> base length 21
• 44 units -> base length 22

First option is not feasible, because you can't have a base with length 0. Also, remember that in any triangle, the length of a side is strictly smaller than the sum of the lengths of the other two sides. So, the base must be smaller than 22, which excludes the last option.

So, all options are possible except the first and last one.

Answer 2

Letters B, C and D

Explanation:

To answer this question, we must remember the fundamental conditions of the existence of a triangle.

One of these conditions is that the measurement on either side is less than the sum of the measurements on the other two.

In other words, the base of this triangle must be less than 22, since the triangle of the question is isosceles and we know that two of its sides measure 11.

So this condition makes option E unviable.

In addition, option A is also impossible since for this to happen the base should measure 0.

Another necessary condition is that the measurement of either side must be greater than the absolute value of the difference between the other two.

Finally, viable options are Letters B, C, and D