Final answer:
The length of the hypotenuse of a right triangle with legs of 3 feet and 4 feet is found using the Pythagorean theorem, resulting in a hypotenuse of 5 feet.
Step-by-step explanation:
The question concerns the length of the hypotenuse of a right-angled triangle when the lengths of the other two sides, or 'legs', are given. In particular, the triangle in question has legs of 3 feet and 4 feet.
To find the hypotenuse, we use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This can be written as:
a² + b² = c²
Plugging in the known values:
3² + 4² = c²
9 + 16 = c²
25 = c²
Now, to find the length of the hypotenuse (c), we take the square root of both sides:
c = √25
c = 5 feet
Therefore, the length of the hypotenuse of this triangle is 5 feet, making option b) the correct answer.