Question

In AEFG, EF = 44 centimeters and FG = 12 centimeters. Which of the following best describes the possible length, in centimeters, of

AO 44 B. O 32 CO 12 D. 32 < EG < 44

Answer 1

The best inequality describes the possible length of EG is 32 < EG < 56 ⇒ B

Explanation:

In any triangle

• The sum of the lengths of any two sides must be greater than the length of the third side

• The length of any side is greater than the difference between the lengths of the other two sides

In Δ EFG

∵ EF = 44 cm

∵ FG = 12 cm

→ Find their sum and difference

∴ The sum of their length = 44 + 12 = 56 cm

∴ The difference between their length = 44 - 12 = 32 cm

→ By using the rule above

∵ EG is the third side

∴ EG < 56

∴ EG > 32

→ Write them in one inequality

∴ 32 < EG < 56

∴ The best inequality describes the possible length of EG is 32 < EG < 56