Directions: Using the digits 1 through 6 at most one time each, place a digit in each box to find three side lengths that are two-digits each and form an acute triangle. Source: Samantha Cruz

Directions: Using the digits 0 to 9, at most one time each, fill in the boxes to find the lengths of the missing sides such that the missing leg’s length is as long as possible. Source: Robert Kaplinsky

Directions: Using the digits 0 to 9, at most one time each, fill in the boxes to find two pairs of possible lengths for the missing sides. Source: Robert Kaplinsky

Directions: What could the lengths of the legs be such that the lengths of the legs are integers and x is an irrational number between 5 and 7? Source: Daniel Luevanos

Directions: What could the lengths of the legs be such that the lengths are integers and x is an irrational number between 5 and 7? Source: Daniel Luevanos

Directions: Find the length of side x in the diagram below Source: Dylan Kane

Directions: Using the digits 0 to 9 at most one time each, place a digit in each box to find an odd modulus, an even modulus, and the smallest possible modulus. Source: Mark Ward

Directions: Using the values 8, 10, 12, 14, 16, 18, and 20, determine lengths for an acute triangle, a right triangle, an obtuse triangle, and a non-triangle. Source: Jonathan Lees

Directions: Using the digits 0 to 9 at most one time each, fill in the boxes to create a square with one of the vertices at (2,3). Source: John Mahlstedt