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

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