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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?

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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. 

The sum of the length of any two sides of the triangle should be always greater than the third side.

Thus, the third side of the triangle must be greater than 7 feet.

What is a triangle?

It is a polygon that has three sides and three vertices. and the sum of the internal angle is 180 degrees.

What is the isosceles triangle?

It is the triangle whose two sides are equal and their opposite angles are also equal.

Given

Let the AB and AC be equal is x feet

And BC is 14 feet.

We know that,

The sum of the length of any two sides of the triangle should be always greater than the third side.

According to the theorem.

[tex]\begin{aligned} \rm x+x & > 14\\\rm x & > 7\\\end{aligned}[/tex]

If the inequality is solved then the value of x will always be greater than 7.

Thus, the third side of the triangle must be greater than 7 feet.

More about the triangles link is given below.

https://brainly.com/question/25813512

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