Question

A parallelogram has two 19-inch sides and two 23-inch sides. What is the range of possible lengths for the diagonals of this parallelogram?

Answer 1

• Between 4 and 42 inches

Explanation:

The two sides and diagonal make a triangle.

Let the diagonal is d, use triangle inequality:

• 19 + 23 > d ⇒ 42 > d ⇒ d < 42
• 19 + d > 23 ⇒ d > 23 - 19 ⇒ d > 4
• 23 + d > 19 ⇒ d > 0

Solution is:

• 4 < d < 42