Question

1. workers at a construction company are building a triangular enclosure. they already have two pieces of wood measuring 72 inches and 96 inches. the list shows several possible lengths for a third piece of wood, except for two. which two lengths cannot be used to complete the triangle?

a. 24 inches
b. 50 inches
c. 93 inches
d. 140 inches
e. 170 inches

Explanation:

Step1: Find valid length range

Let the third side be $x$. By triangle inequality:
$$96 - 72 < x < 96 + 72$$
$$24 < x < 168$$

Step2: Check each option

• A. 24: $24

ot> 24$, invalid

• B. 50: $24 < 50 < 168$, valid
• C. 93: $24 < 93 < 168$, valid
• D. 140: $24 < 140 < 168$, valid
• E. 170: $170

ot< 168$, invalid

Answer:

A. 24 inches, E. 170 inches