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 2 and Shelf 4

Shelf 1 and Shelf 2

Shelf 1 and Shelf 3

Shelf 3 and Shelf 4

Answer 1

@dpaInc @phi

Answer 2

@Callisto @Luis_Rivera

Answer 3

use the triangle inequality: a + b > c, where a, b, c are the sides of the triangle.
for each case, check that the sum of ANY two sides have to be bigger than the third.
you'll find that 2 of those shelves can't be made...