Question

Elijah drew a triangle that has one side longer than the other two. What must be true about the lengths of the sides of Elijah’s triangle?

A. The sum of the two shorter side lengths must be less than the length of the longest side.

C. The product of the two shorter side lengths must be less than the length of the longest side.

B. The sum of the two shorter side lengths must be greater than the length of the longest side.

D. The product of the two shorter side lengths must be greater than the length of the longest side.

Answer 1

B. The sum of the two shorter side lengths must be greater than the length of the longest side.

Explanation:

To form a triangle, the longest side should be less than the sum of two shorter sides

Answer 2

B. The sum of the two shorter side lengths must be greater than the length of the longest side.

Explanation:

All triangles must follow the Triangle Inequality Theorem, which states that for a triangle with sides a, b, and c:

a + b > c

a + c > b

b + c > a

Here, we can say that the two shorter sides are a and b and the longer side is c. So, they must satisfy the Triangle Inequality Theorem, which state that:

a + b > c

Looking at the answer choices, the only one that matches the above description is B (not sure why B comes after C, but...).

Hope this helps!