Question

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

Shelf 1: 6 inches, 14 inches, 21 inches
Shelf 2: 10 inches, 15 inches, 24 inches
Shelf 3: 11 inches, 20 inches, 32 inches
Shelf 4: 8 inches, 20 inches, 24 inches

Which of the above shelf dimensions are not possible?

Shelf 2 and Shelf 4

Shelf 1 and Shelf 3

Shelf 1 and Shelf 2

Shelf 3 and Shelf 4

Answer 1

If you have a triangle that has the dimensions a, b, c, to be possible:\[a<b+c\]\[b<a+c\]\[c<a+b\].

So, testing Shelf 1:
6 < 14 + 21 (true)
14 < 21 + 6 (true)
21 < 20 (false)

Shelf 1 its not possible.

Testing Shelf 2:
10 < 15 + 24 (true)
15 < 10 + 24 (true)
24 < 10 + 15 (true)

Shelf 2 is possible.

Testing Shelf 3:
11 < 20 + 32 (true)
20 < 11 + 32 (true)
32 < 20 + 11 (false)

Shelf 3 is not possible.

Testing Shelf 4:
8 < 20 + 24 (true)
20 < 24 + 8 (true)
24 < 20 + 8 (true)

Shelf 4 is possible.

So, the answers of the shelf's that isn't possible is:
Shelf 1 and Shelf 3.