Question

Part of a large metal sculpture will be a triangle formed by welding three bars together. The artist has four bars that measure 12 feet, 7 feet, 5 feet, and 3 feet. Which bar could not be used with two of the others to form a triangle?

Answer 1

The 12 feet bar cannot be used with 5 feet and 3 feet bar to form a triangle.

Explanation:

According to the Triangle Inequality theorem the sum of any two sides must be greater than or equal to the third side of the triangle.

In this case if we chose the 3 bars to be 12 feet,5 feet and 3 feet, the sum of 3 and 5 would be 8 feet which is less than the third side i.e. 12 feet which does not obey the triangle inequality theorem, hence a triangle cannot be built with these side lengths.

Therefore, the 12 feet bar cannot be used with 5 feet and 3 feet bar to form a triangle.