Question

Two sides of a triangle have lengths 7 and 17. Which expression describes the length of the third side?

Options:
A. at least 10 and less than 24
B. greater than 10 and at most 24
C. at least 10 and at most 24
D. greater than 10 and less than 24

Answer 1

The length of the third side of a triangle with sides of 7 and 17 must be greater than 10 and less than 24, following the Triangle Inequality Theorem.

Step-by-step explanation:

The question regarding the length of the third side of a triangle with two known side lengths involves understanding the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, the third side must be longer than the difference between the two known side lengths and shorter than their sum.

Given the lengths of 7 and 17, the third side must be:

• Greater than 17 - 7 = 10
• Less than 17 + 7 = 24

Therefore, the correct answer is D. greater than 10 and less than 24.