which of the following sets of three links could be the sides of a right triangle?
15in, 15in, 30in
11in, 60in, 61in
13in, 38in, 51in
17in, 17in, 17in
11in, 60in, 61in (satisfies the Pythagorean Theorem: 11^2 + 60^2 = 61^2)
To determine which sets of three links could be the sides of a right triangle, we can use the Pythagorean theorem.
The Pythagorean theorem 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 lengths of the other two sides.
Let's calculate the values for each set of links:
Set 1: 15in, 15in, 30in
15^2 + 15^2 = 225 + 225 = 450
30^2 = 900
The sum of the squares of the two shorter sides (450) is not equal to the square of the longest side (900). Therefore, this set of links cannot form a right triangle.
Set 2: 11in, 60in, 61in
11^2 + 60^2 = 121 + 3600 = 3721
61^2 = 3721
The sum of the squares of the two shorter sides (3721) is equal to the square of the longest side (3721). Therefore, this set of links can form a right triangle.
Set 3: 13in, 38in, 51in
13^2 + 38^2 = 169 + 1444 = 1613
51^2 = 2601
The sum of the squares of the two shorter sides (1613) is not equal to the square of the longest side (2601). Therefore, this set of links cannot form a right triangle.
Set 4: 17in, 17in, 17in
17^2 + 17^2 = 289 + 289 = 578
17^2 = 289
The sum of the squares of the two shorter sides (578) is equal to the square of the longest side (289). Therefore, this set of links can form a right triangle.
In conclusion, the sets of links that could be the sides of a right triangle are:
1) 11in, 60in, 61in
2) 17in, 17in, 17in
To determine whether a set of three links could be the sides of a right triangle, we need to apply the Pythagorean theorem. According to this theorem, 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 lengths of the other two sides.
Let's calculate using the Pythagorean theorem with each set of three links:
1) 15in, 15in, 30in:
In this case, the longest side is 30in, which is the hypotenuse. The other two sides are both 15in. We can use the Pythagorean theorem to check if it holds:
15^2 + 15^2 = 225 + 225 = 450
30^2 = 900
Since 450 is not equal to 900, this set of links does not form a right triangle.
2) 11in, 60in, 61in:
Here, the longest side is 61in, and the other two sides are 11in and 60in:
11^2 + 60^2 = 121 + 3600 = 3721
61^2 = 3721
Since 3721 is equal to 3721, this set of links does form a right triangle.
3) 13in, 38in, 51in:
In this case, the longest side is 51in, and the other two sides are 13in and 38in:
13^2 + 38^2 = 169 + 1444 = 1613
51^2 = 2601
Since 1613 is not equal to 2601, this set of links does not form a right triangle.
4) 17in, 17in, 17in:
This set of links would form an equilateral triangle, which is also a right triangle since all the angles are 60 degrees. Thus, this set of links does form a right triangle.
To summarize:
- The set 11in, 60in, 61in forms a right triangle.
- The other sets (15in, 15in, 30in; 13in, 38in, 51in; 17in, 17in, 17in) do not form right triangles.