Question

determining possible side lengths
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?
( x>) feet

Explanation:

Step1: Recall Triangle Inequality Theorem

For a triangle with side lengths \(a\), \(b\), and \(c\), the sum of any two sides must be greater than the third side. In an isosceles triangle with two congruent sides \(x\) and base \(14\) feet, we apply the triangle inequality: \(x + x>14\).

Step2: Solve the Inequality

Simplify \(x + x>14\) to \(2x>14\). Divide both sides by \(2\): \(\frac{2x}{2}>\frac{14}{2}\), which gives \(x > 7\).

Answer:

\(7\)