Drag and drop the given set of measurements into the correct box to describe whether the measurements can describe the lengths of the three sides of a right triangle or not.(3 points)
Could be the Sides of a Right Triangle Cannot be the Sides of a Right Triangle
63in, 16, 65 in. 29 in, 20 in, 21 in 4m, 5 m, 6 m
Could be the Sides of a Right Triangle:
29 in, 20 in, 21 in
Cannot be the Sides of a Right Triangle:
63in, 16, 65 in.
4m, 5 m, 6 m
Could be the Sides of a Right Triangle: 29 in, 20 in, 21 in
Cannot be the Sides of a Right Triangle: 63in, 16, 65 in
Cannot be the Sides of a Right Triangle: 4m, 5m, 6m
To determine whether a set of measurements can describe the lengths of the three sides of a right triangle, we need to apply 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 other two sides.
Let's apply this concept to each set of measurements:
1. 63in, 16, 65in:
To determine if this could be the sides of a right triangle, we need to check if 65^2 is equal to 63^2 + 16^2.
Calculating:
65^2 = 4225
63^2 + 16^2 = 3969 + 256 = 4225
Since the two values are equal, the measurements of 63in, 16, 65in could be the sides of a right triangle.
2. 29in, 20in, 21in:
To determine if this could be the sides of a right triangle, we need to check if 29^2 is equal to 20^2 + 21^2.
Calculating:
29^2 = 841
20^2 + 21^2 = 400 + 441 = 841
Since the two values are equal, the measurements of 29in, 20in, 21in could be the sides of a right triangle.
3. 4m, 5m, 6m:
To determine if this could be the sides of a right triangle, we need to check if 6^2 is equal to 4^2 + 5^2.
Calculating:
6^2 = 36
4^2 + 5^2 = 16 + 25 = 41
Since the two values are not equal, the measurements of 4m, 5m, 6m cannot be the sides of a right triangle.
Therefore, the correct box to place each set of measurements is:
Could be the Sides of a Right Triangle:
- 63in, 16, 65in
- 29in, 20in, 21in
Cannot be the Sides of a Right Triangle:
- 4m, 5m, 6m
is this correct
Apologies for the incorrect response earlier. Let's go through the correct analysis for the given sets of measurements:
1. 63in, 16, 65in:
To determine if this could be the sides of a right triangle, we need to check if 65^2 is equal to 63^2 + 16^2.
Calculating:
65^2 = 4225
63^2 + 16^2 = 3969 + 256 = 4225
Since the two values are equal, the measurements of 63in, 16, 65in could be the sides of a right triangle.
2. 29in, 20in, 21in:
To determine if this could be the sides of a right triangle, we need to check if 29^2 is equal to 20^2 + 21^2.
Calculating:
29^2 = 841
20^2 + 21^2 = 400 + 441 = 841
Since the two values are equal, the measurements of 29in, 20in, 21in could be the sides of a right triangle.
3. 4m, 5m, 6m:
To determine if this could be the sides of a right triangle, we need to check if 6^2 is equal to 4^2 + 5^2.
Calculating:
6^2 = 36
4^2 + 5^2 = 16 + 25 = 41
Since the two values are not equal, the measurements of 4m, 5m, 6m cannot be the sides of a right triangle.
Therefore, the correct box to place each set of measurements is:
Could be the Sides of a Right Triangle:
- 63in, 16, 65in
- 29in, 20in, 21in
Cannot be the Sides of a Right Triangle:
- 4m, 5m, 6m
Apologies for the confusion caused by the initial response.