Final answer:
The length of Mr. Holloway's ladder is found using the Pythagorean theorem. Considering the height of 4m and the base distance of 5m, the ladder's length is calculated to be approximately 6.4 meters when rounded to the nearest tenth.
Step-by-step explanation:
Finding the Length of a Ladder Resting Against a Wall
To find the length of the ladder that Mr. Holloway is using to reach the roof, we can use the Pythagorean theorem. The ladder forms a right triangle with the ground and the wall of the house. The vertical distance from the ground to the roof (height) is 4 meters and the horizontal distance from the base of the ladder to the wall (base) is 5 meters.
Let L represent the length of the ladder. The Pythagorean theorem 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 other two sides (a and b). This can be written as:
c² = a² + b²
In this case:
L² = 4² + 5²
L² = 16 + 25
L² = 41
L = √41
L ≈ 6.4 meters (rounded to the nearest tenth)
Therefore, the ladder that Mr. Holloway is using is approximately 6.4 meters long when rounded to the nearest tenth.