Respuesta :
Answer:
To find the length of \( \overline{FD} \) in the given scenario, we can apply the Pythagorean Theorem since \( \overline{FD} \) represents the hypotenuse of a right triangle.
Let's represent the lengths of the sides of the triangle as follows:
- \( \overline{CA} = 19 \)
- \( \overline{AB} = 25 \)
- \( \overline{DE} = 55 \)
We know that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. Therefore, we can set up the following equation:
\[ \overline{CA}^2 + \overline{AB}^2 = \overline{DE}^2 \]
Substitute the given values:
\[ 19^2 + 25^2 = \overline{FD}^2 \]
\[ 361 + 625 = \overline{FD}^2 \]
\[ 986 = \overline{FD}^2 \]
To find the length of \( \overline{FD} \), we need to take the square root of 986:
\[ \overline{FD} = \sqrt{986} \]
\[ \overline{FD} \approx 31.4 \]
Therefore, the length of \( \overline{FD} \) is approximately 31.4 units.
I hope this helps you!
