Mr. anderson is building a triangular-shaped roof for his shed. the triangle must be isosceles with its base (noncongruent) side measuring 14 feet. the length of one of the congruent legs must be greater than what value?

In Geometry, there exists a theorem called Triangle Inequality Theorem which states that the sum of the lengths of any two sides of the triangle should be always greater than the third side. For this item, let x be the congruent sides such that the inequality theorem will be mathematically expressed as,
                                              x + x > 14
Solving for the value of x in the inequality will give us an answer of x > 7. Thus, the side of the congruent side of the triangle should be greater than 7 feet.