A baseball infield is a square, each side measuring 90 feet. To the nearest foot, what is the distance from home plate to second base?
101 feet
113 feet
127 feet
139 feet
The distance from home plate to second base is the same as the length of the diagonal of the square infield.
Using the Pythagorean Theorem, we can calculate the length of the diagonal:
d^2 = 90^2 + 90^2
d^2 = 8100 + 8100
d^2 = 16200
d ≈ √16200
d ≈ 127.3 feet
To the nearest foot, the distance from home plate to second base is 127 feet.
Therefore, the correct answer is 127 feet.
Janet leaves home for her school. She walks 6 blocks north and then 8 blocks west. How far is she from the school?
2 blocks
4 blocks
6 blocks
10 blocks
To find out how far Janet is from her school, we can use the Pythagorean theorem.
Janet walks 6 blocks north and 8 blocks west, forming a right-angled triangle.
The distance from the school can be calculated using the formula:
distance^2 = (6^2) + (8^2)
distance^2 = 36 + 64
distance^2 = 100
distance = √100
distance = 10 blocks
Therefore, Janet is 10 blocks away from her school.
The correct answer is 10 blocks.
Elisa designed a flower garden in the shape of a square with a side length of 10 feet. She plans to build a walkway along the diagonal. What is the closest measure of the length of the walkway?
12.12 feet
13.13 feet
14.14 feet
15.14 feet
To find the length of the walkway, we can use the Pythagorean theorem.
The diagonal of a square divides it into two congruent right-angled triangles.
In this case, the square has a side length of 10 feet, so each right-angled triangle has a base and height of 10 feet.
Using the Pythagorean theorem, we can calculate the length of the diagonal (walkway):
length^2 = (10^2) + (10^2)
length^2 = 100 + 100
length^2 = 200
length ≈ √200
length ≈ 14.14 feet
Therefore, the closest measure of the length of the walkway is 14.14 feet.
So, the correct answer is 14.14 feet.
Find the distance between two points (-6, 3) and (9, 12).
306−−−√ units
340−−−√ units
280−−−√ units
148−−−√ units
To find the distance between two points, we can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates (-6, 3) and (9, 12), we can substitute the values into the formula:
Distance = √((9 - (-6))^2 + (12 - 3)^2)
Distance = √((9 + 6)^2 + (12 - 3)^2)
Distance = √(15^2 + 9^2)
Distance = √(225 + 81)
Distance = √306
Therefore, the distance between the two points is √306 units.
The closest option is 306−−−√ units, so the correct answer is 306−−−√ units.
Find the radius of a circle using the Pythagorean theorem, given that the center is at (18, 5) and the point (22, 8) lies on the circle.
8 units
12 units
5 units
10 units
To find the radius of a circle, we can use the distance formula between the center of the circle and a point on the circle.
Using the coordinates (18, 5) for the center and (22, 8) for the point on the circle, we can substitute the values into the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance = √((22 - 18)^2 + (8 - 5)^2)
Distance = √(4^2 + 3^2)
Distance = √(16 + 9)
Distance = √25
Distance = 5
Therefore, the radius of the circle is 5 units.
The closest option is 5 units, so the correct answer is 5 units.
Find the radius of a circle using the Pythagorean theorem, given that the center is at (11, -3) and the point (3, 12) lies on the circle.
14 units
17 units
19 units
√17 units
To find the radius of a circle, we can use the distance formula between the center of the circle and a point on the circle.
Using the coordinates (11, -3) for the center and (3, 12) for the point on the circle, we can substitute the values into the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance = √((3 - 11)^2 + (12 - (-3))^2)
Distance = √((-8)^2 + (15)^2)
Distance = √(64 + 225)
Distance = √289
Distance = 17
Therefore, the radius of the circle is 17 units.
The closest option is 17 units, so the correct answer is 17 units.
You're locked out of your house and the only open window is on the second floor, 12 feet above the ground. You need to borrow a ladder from one of your neighbors. There's a bush along the edge of the house, so you'll have to place the ladder 35 feet from the house. What length of ladder do you need to reach the window?
To calculate the length of the ladder needed to reach the window, we can use the Pythagorean theorem. The ladder length will be the hypotenuse of a right triangle formed by the height of the window (12 feet), the distance from the house (35 feet), and the ladder itself.
Using the Pythagorean theorem:
ladder length^2 = window height^2 + distance from the house^2
ladder length^2 = 12^2 + 35^2
ladder length^2 = 144 + 1225
ladder length^2 = 1369
ladder length = √1369
ladder length ≈ 36.97 feet
Therefore, you would need a ladder approximately 36.97 feet long to reach the window.
Rounded to the nearest foot, the length of the ladder needed would be 37 feet.
You're locked out of your house and the only open window is on the second floor, 34 feet above the ground. You need to borrow a ladder from one of your neighbors. There's a bush along the edge of the house, so you'll have to place the ladder 41 feet from the house. What length of ladder do you need to reach the window?
To calculate the length of the ladder needed to reach the window, we can use the Pythagorean theorem. The ladder length will be the hypotenuse of a right triangle formed by the height of the window (34 feet), the distance from the house (41 feet), and the ladder itself.
Using the Pythagorean theorem:
ladder length^2 = window height^2 + distance from the house^2
ladder length^2 = 34^2 + 41^2
ladder length^2 = 1156 + 1681
ladder length^2 = 2837
ladder length ≈ √2837
ladder length ≈ 53.27 feet
Therefore, you would need a ladder approximately 53.27 feet long to reach the window.
Rounded to the nearest foot, the length of the ladder needed would be 53 feet.
The dimensions of a room are 85 ft by 56 ft, respectively. Find the length across the diagonal of the room to the nearest whole number.
To find the length of the diagonal of the room, we can use the Pythagorean theorem. The diagonal will be the hypotenuse of a right triangle formed by the length and width of the room.
Using the Pythagorean theorem:
diagonal^2 = length^2 + width^2
diagonal^2 = 85^2 + 56^2
diagonal^2 = 7225 + 3136
diagonal^2 = 10361
diagonal ≈ √10361
diagonal ≈ 101.8
Therefore, the length across the diagonal of the room is approximately 101.8 feet.
Rounding to the nearest whole number, the length across the diagonal of the room would be 102 feet.
Find the radius of a circle using the Pythagorean theorem, given that the center is at (3, 4) and the point (5, 6) lies on the circle.
8√ units
8 units
164−−−√ units
39−−√ units
To find the radius of a circle, we can use the distance formula between the center of the circle and a point on the circle.
Using the coordinates (3, 4) for the center and (5, 6) for the point on the circle, we can substitute the values into the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance = √((5 - 3)^2 + (6 - 4)^2)
Distance = √(2^2 + 2^2)
Distance = √(4 + 4)
Distance = √8
Therefore, the radius of the circle is √8 units.
The closest option is 8√ units, so the correct answer is 8√ units.