If someone is attached to a 20 ft rope, which is attached to the corner of a building, how far can they move? If the bulding is 22 ft X 15 ft?
The way you worded the question, the answer is 20 ft
I have seen this question worded in the following way:
A dog with a 20 ft leash is tied to the corner of a building which is 22 ft by 15ft.
What is the area that the dog can cover?
make a sketch.
clearly he can reach 20 ft down along the building.
If he goes the other way, he can move around the corner, cover the 15 ft along the width of the building and wrap around another 5 ft down the length of the opposite side of the long building
So I see 3/4 of a circle with radius 20, and 1/4 of a circle with radius 5
total area = (3/4)π(20)^2 + (1/4)π(5^2)
= 300π + (25/4)π = (1225/4)π or 306.25π or appr 962 ft^2
To calculate how far someone can move while being attached to a rope, which is attached to a corner of a building, we need to determine the largest possible area available for movement.
In this scenario, the person is attached to a 20 ft rope, and the building is 22 ft wide and 15 ft tall. The rope forms the hypotenuse of a right-angled triangle, where the building's sides act as the two perpendicular sides. The corner where the rope is attached serves as the right angle of the triangle.
We can use the Pythagorean theorem to find the length of the hypotenuse (the rope). The formula is:
c^2 = a^2 + b^2
where c represents the hypotenuse and a and b represent the perpendicular sides.
In this case, a = 22 ft and b = 15 ft. Let's calculate the length of the hypotenuse (c) using the formula:
c^2 = 22^2 + 15^2
c^2 = 484 + 225
c^2 = 709
Taking the square root of both sides to solve for c:
c ≈ 26.63 ft
So, the length of the rope (hypotenuse) is approximately 26.63 ft. Since the person is attached to this rope, they can move within a circle with a radius of 26.63 ft. The person can move anywhere within this circle.
To calculate the Area (A) of the circle, we use the formula:
A = π * r^2
where π is a mathematical constant (approximately equal to 3.14159) and r is the radius of the circle.
Plugging in the radius value:
A ≈ 3.14159 * (26.63 ft)^2
A ≈ 3.14159 * 708.97 ft^2
A ≈ 2228.02 ft^2
Therefore, the person can move within an area of approximately 2228.02 square feet.