A soccer field is a rectangle 80 meters wide and 100 meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance?
128.06 meters
64.03 meters
82 meters
68 meters
To find the distance from one corner to the corner diagonally across, we can use the Pythagorean theorem.
Let's take one corner of the rectangle as the starting point, and the corner diagonally across as the endpoint of the diagonal.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the width of the soccer field (80 meters) is one side of the right triangle, and the length (100 meters) is the other side. The diagonal is the hypotenuse.
Using the Pythagorean theorem:
Diagonal^2 = Width^2 + Length^2
Diagonal^2 = 80^2 + 100^2
Diagonal^2 = 6400 + 10000
Diagonal^2 = 16400
Taking the square root of both sides:
Diagonal = √16400
Diagonal ≈ 128.06 meters
Therefore, the distance from one corner to the corner diagonally across is approximately 128.06 meters. Therefore, the correct answer is 128.06 meters.
Ronald's home is located 33 miles west and 56 miles north from his hotel. Find the distance from his hotel to his home.
65 miles
80 miles
90 miles
99 miles
To find the distance from Ronald's hotel to his home, we can use the Pythagorean theorem.
Ronald's home is located 33 miles west and 56 miles north from his hotel. We can consider these distances as the two sides of a right triangle, with the distance from the hotel to Ronald's home being the hypotenuse.
Using the Pythagorean theorem:
Distance^2 = West^2 + North^2
Distance^2 = 33^2 + 56^2
Distance^2 = 1089 + 3136
Distance^2 = 4225
Taking the square root of both sides:
Distance = √4225
Distance = 65 miles
Therefore, the distance from Ronald's hotel to his home is 65 miles. Thus, the correct answer is 65 miles.
The park is 18 miles east of my home. The library is 12 miles north of the park. How far is my home from the library?
35 miles
21.6 miles
8.2 miles
18.6 miles
To find the distance from your home to the library, we can use the Pythagorean theorem.
Given that the park is 18 miles east of your home and the library is 12 miles north of the park, we can consider these distances as the two sides of a right triangle, with the distance from your home to the library being the hypotenuse.
Using the Pythagorean theorem:
Distance^2 = East^2 + North^2
Distance^2 = 18^2 + 12^2
Distance^2 = 324 + 144
Distance^2 = 468
Taking the square root of both sides:
Distance ≈ √468
Distance ≈ 21.6 miles
Therefore, the distance from your home to the library is approximately 21.6 miles. Thus, the correct answer is 21.6 miles.
Sam buys a carpet for his apartment. The diagonal length of the carpet is 12 feet and the width is 10 feet. Find the length of the carpet.
8 feet
6.633 feet
3 feet
4.5 feet
To find the length of the carpet, we can use the Pythagorean theorem.
Let's consider the width of the carpet (10 feet) as one side of a right triangle, and the length of the carpet as the other side. The diagonal length of the carpet (12 feet) is the hypotenuse.
Using the Pythagorean theorem:
Hypotenuse^2 = Width^2 + Length^2
(12 feet)^2 = (10 feet)^2 + Length^2
144 feet^2 = 100 feet^2 + Length^2
Length^2 = 144 feet^2 - 100 feet^2
Length^2 = 44 feet^2
Taking the square root of both sides:
Length ≈ √44 feet
Length ≈ 6.633 feet
Therefore, the length of the carpet is approximately 6.633 feet. Thus, the correct answer is 6.633 feet.