Question

Suppose a triangle has two sides that measure 7 inches and 11 inches. Which of the following could be the length of the third side? Select all that apply.

A.4 inches
B. 7 inches
C. 13.5 inches
D. 18 inches
E. 20 inches

Answer 1

Using the Triangle Inequality Theorem, the third side of a triangle with two sides measuring 7 inches and 11 inches must be longer than 4 inches and shorter than 18 inches. Hence, option B (7 inches) and option C (13.5 inches) could be the lengths of the third side.

Step-by-step explanation:

To determine the length of the third side of a triangle when given the lengths of two sides, we can use 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. Similarly, the difference between the lengths of any two sides must be less than the length of the third side.

For a triangle with sides of 7 inches and 11 inches, the third side must be longer than 4 inches (11 - 7) and shorter than 18 inches (11 + 7). So, we can eliminate options D (18 inches) and E (20 inches), as they are too long, and option A (4 inches), as it is too short.

This leaves us with options B (7 inches) and C (13.5 inches), which both fall within the range determined by the Triangle Inequality Theorem.

Answer 2

You need to know the rule or theorem for the lengths of the sides of a triangle,which is: the lengths of any two sides of a triangle must add up to more than the length of the third side.

So, let's examine each option:

A.4 inches => side A: 7, side B: 11, side C: 4 ---> NOT POSSIBLE

Justification:

7 + 4 = 11

11 = 11 => the sum of sides A and C is not greter than the side B, so it does not satisfy the rule.


B. 7 inches => side A: 7, side B: 11, side C: 7. ---> COULD BE

Justification:

7 + 7 = 14; 14 > 11
7 + 11 = 18; 18 > 7


C. 13.5 inches => side A: 7, side B: 11, side C: 13.5: ---> COULD BE

Justification:

7 + 11 = 18; 18 > 13.5
7 + 13.5 = 20.5; 20.5 > 11
11+13.5 = 24.5; 24.5 > 7

D. 18 inches => side A: 7, side B: 11, side C: 18 ---> NOT POSSIBLE

Justification:

7 + 11 = 18; 18 = 18 => it does not satisfy the rule.

E. 20 inches => side A: 7, side B: 11, side C: 20 ---> NOT POSSIBLE

Justification:

7 + 11 = 18; 18 < 20 => it does not satisfy the rule