Question

Mr. Anderson is building a triangular-shaped roof for his shed. The triangle must be isosceles with its base (noncongruent) side measuring 14 feet.

A triangle has a base length of 14 feet. The other 2 sides have a length of x.

The length of one of the congruent legs must be greater than what value?

x >
feet

Answer 1

To find the minimum length of the congruent sides (\( x \)) of an isosceles triangle with a base of 14 feet, we can use the triangle inequality theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

In our triangle, let’s denote the sides as follows:

- The base (non-congruent side) = 14 feet
- The length of each of the congruent legs = \( x \)

According to the triangle inequality, we must satisfy the following conditions:

1. \( x + x > 14 \) (the sum of the two congruent sides must be greater than the base)
2. \( x + 14 > x \) (this condition is always satisfied since 14 is a positive length)
3. \( 14 + x > x \) (this is also always true since \( 14 > 0 \))

Now, focusing on the first condition:

\[
2x > 14
\]

Dividing both sides by 2 gives:

\[
x > 7
\]

Thus, the length of one of the congruent legs must be greater than \( 7 \) feet.

So the answer is:

\[
x > 7 \text{ feet}
\]