(7, 8, 9) is a Pythagorean triplet. Choose the correct statement from the following.
(7, 8, 9) is a Pythagorean triplet since it satisfies the Pythagorean theorem.
(7, 8, 9) is a not a Pythagorean triplet since it satisfies the Pythagorean theorem.
(7, 8, 9) is a Pythagorean triplet since it does not satisfy the Pythagorean theorem.
(7, 8, 9) is a not a Pythagorean triplet since it does not satisfy the Pythagorean theorem.
(7, 8, 9) is a Pythagorean triplet since it satisfies the Pythagorean theorem.
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 between your home and the library, you can use the Pythagorean theorem.
Let's assume the distance between your home and the library is "x" miles.
We have a right-angled triangle where the side lengths are 18 miles (east), x miles (hypotenuse), and 12 miles (north).
Applying the Pythagorean theorem:
x^2 = 18^2 + 12^2
x^2 = 324 + 144
x^2 = 468
x ≈ 21.6 miles
Therefore, the distance between your home and the library is approximately 21.6 miles.
Martha climbs 40 steps to reach the first floor of a building. If the vertical and horizontal distance of each step is 1.5 ft and 1 ft, find the distance between the start and end points of each step.
1 ft
1.5 ft
1.8 ft
40 ft
To find the distance between the start and end points of each step, we need to use the Pythagorean theorem.
Let's assume the vertical distance of each step is "a" ft and the horizontal distance of each step is "b" ft.
Using the Pythagorean theorem, we have:
c^2 = a^2 + b^2
In this case, a = 1.5 ft and b = 1 ft.
c^2 = (1.5)^2 + (1)^2
c^2 = 2.25 + 1
c^2 = 3.25
c ≈ 1.8028 ft
Therefore, the distance between the start and end points of each step is approximately 1.8028 ft. Rounded to the nearest tenth, it would be 1.8 ft.
Mike bought a photo frame which measured 8 inches in length and 7 inches in width. Determine the diagonal length of the photo frame.
63 inches
49 inches
10.63 inches
113 inches
To determine the diagonal length of the photo frame, we can use the Pythagorean theorem.
Let's assume the length of the photo frame is "L" inches and the width is "W" inches.
Using the Pythagorean theorem, we have:
diagonal^2 = length^2 + width^2
In this case, L = 8 inches and W = 7 inches.
diagonal^2 = 8^2 + 7^2
diagonal^2 = 64 + 49
diagonal^2 = 113
diagonal ≈ √113 ≈ 10.63 inches
Therefore, the diagonal length of the photo frame is approximately 10.63 inches.
Anthony had to travel 24 miles north and then 7 miles west. Find the shortest distance between the starting and the end points.
30 miles
36 miles
25 miles
39 miles
To find the shortest distance between the starting and end points, we can use the Pythagorean theorem.
Let's assume the distance traveled north is "a" miles and the distance traveled west is "b" miles.
Using the Pythagorean theorem, we have:
shortest distance^2 = (distance north)^2 + (distance west)^2
In this case, a = 24 miles and b = 7 miles.
shortest distance^2 = 24^2 + 7^2
shortest distance^2 = 576 + 49
shortest distance^2 = 625
shortest distance = √625 = 25 miles
Therefore, the shortest distance between the starting and end points is 25 miles.
Mike bought a photo frame which measured 56 inches in length and 33 inches in width. Determine the diagonal length of the photo frame.
To determine the diagonal length of the photo frame, we can use the Pythagorean theorem.
Let's assume the length of the photo frame is "L" inches and the width is "W" inches.
Using the Pythagorean theorem, we have:
diagonal^2 = length^2 + width^2
In this case, L = 56 inches and W = 33 inches.
diagonal^2 = 56^2 + 33^2
diagonal^2 = 3136 + 1089
diagonal^2 = 4225
diagonal = √4225 = 65 inches
Therefore, the diagonal length of the photo frame is 65 inches.
Which of the following can be the sides of a right triangle?
0.5 cm, 2.1 cm, 3 cm
1.1 cm, 6 cm, 6.1 cm
2 cm, 2.2 cm, 2.5 cm
4.2 cm, 5.6 cm, 7.5 cm
To determine if a set of side lengths can form a right triangle, we need to check if the lengths satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's evaluate each set of side lengths:
1) For (0.5 cm, 2.1 cm, 3 cm):
In this case, 3^2 = 9 is not equal to 0.5^2 + 2.1^2 = 0.25 + 4.41 = 4.66. Therefore, this set of side lengths cannot form a right triangle.
2) For (1.1 cm, 6 cm, 6.1 cm):
In this case, 6.1^2 = 37.21 is not equal to 1.1^2 + 6^2 = 1.21 + 36 = 37.21. Therefore, this set of side lengths cannot form a right triangle.
3) For (2 cm, 2.2 cm, 2.5 cm):
In this case, 2.5^2 = 6.25 is equal to 2^2 + 2.2^2 = 4 + 4.84 = 8.84. Therefore, this set of side lengths can form a right triangle.
4) For (4.2 cm, 5.6 cm, 7.5 cm):
In this case, 7.5^2 = 56.25 is equal to 4.2^2 + 5.6^2 = 17.64 + 31.36 = 49. Therefore, this set of side lengths can form a right triangle.
Therefore, the correct answer is:
(2 cm, 2.2 cm, 2.5 cm)
(4.2 cm, 5.6 cm, 7.5 cm)
A disk is in the form of square and measures 5.25 inches on each side. Find the diagonal length of the disk.
7.4 inches
6.5 inches
5.5 inches
4.5 inches
To find the diagonal length of the square disk, we can use the Pythagorean theorem.
Let's assume the side length of the square disk is "s" inches.
Using the Pythagorean theorem, we have:
diagonal^2 = side length^2 + side length^2
In this case, the side length is 5.25 inches.
diagonal^2 = 5.25^2 + 5.25^2
diagonal^2 = 27.56 + 27.56
diagonal^2 = 55.12
diagonal ≈ √55.12 ≈ 7.42 inches
Therefore, the diagonal length of the disk is approximately 7.42 inches. Rounded to the nearest tenth, it would be 7.4 inches.
If the lengths of two legs of a right triangle are 2, then what is the length of its hypotenuse?
2.83
4
1.33
0.14
To find the length of the hypotenuse of a right triangle given the lengths of the two legs, we can use the Pythagorean theorem.
Let's assume one leg is "a" units long, and the other leg is "b" units long.
The Pythagorean theorem states that for a right triangle, the square of the length of the hypotenuse (denoted as "c") is equal to the sum of the squares of the lengths of the legs.
So, in this case, we have:
c^2 = a^2 + b^2
Given that one leg is 2 units long, we have:
c^2 = 2^2 + b^2
c^2 = 4 + b^2
We are not given the length of the second leg, and as such, we cannot determine the length of the hypotenuse using the information provided.
Therefore, we do not have enough information to determine the length of the hypotenuse.