Short Answer 
To determine the length of the segment cut from a line by two sides of a triangle with a side length of 26 inches, we calculate using the formula d = sqrt((L/2)² + (L/2)²). After simplification, the length of the segment is found to be 13√2 inches.
Step 1: Understand the Problem
We need to determine the length of a segment cut from a line by two sides of a triangle. The side length of the triangle is provided as L = 26 inches. Knowing this, we will calculate the length of the segment using geometric principles.
Step 2: Calculate the Length of the Dividing Line
To find the length (d) of the line that divides the segment, we use the formula: d = sqrt((L/2)² + (L/2)²). This requires us to first calculate (L/2):
- Calculate L/2: 26/2 = 13
- Substitute into the formula: d = sqrt(13² + 13²)
Step 3: Simplify Your Result
Now we simplify the expression for d. Rewrite it as d = sqrt(13² * 2), which leads us to:
- Taking the square root gives: d = 13‚àö2
- This shows that the length of the segment cut from the line is 13‚àö2.