Question

A carpenter proposes to make 4 triangular shelves of the following dimensions:

Shelf 1: 6 inches, 14 inches, 18 inches
Shelf 2: 10 inches, 15 inches, 26 inches
Shelf 3: 11 inches, 20 inches, 25 inches
Shelf 4: 8 inches, 20 inches, 30 inches

Which of the above shelf dimensions are not possible?

Shelf 1 and Shelf 3
Shelf 2 and Shelf 4
Shelf 1 and Shelf 2
Shelf 3 and Shelf 4

Answer 1

does anyone know?

Answer 2

Nvm, it's 2 and 4

Answer 3

To form a triangle, sum of 2 sides must be greater than the 3rd one, that is
a+b>c and b+c>a and c+a>b

Shelf 1: 6 inches, 14 inches, 18 inches
6+14> 18 => true
14+18> 6 => true
6+18 > 14 => true
=> can form a triangle

For shelf 2: 10 inches, 15 inches, 26 inches
10+15 > 26 => Wrong!
=> cannot form a triangle

For shelf 3: 11 inches, 20 inches, 25 inches
11+ 20 > 25 => true
20+25 > 11 => true
11+25 > 20 => true
=> can form a triangle

For shelf 4: 8 inches, 20 inches, 30 inches
8+20 > 30 => wrong!
=> cannot form a triangle