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)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Could Be the Sides of a Right Triangle Cannot Be the Sides of a Right Triangle
Choices
4 m,5 m,6 m
29 in,20 in,21 in
63 in,16 in,21 in
Could Be the Sides of a Right Triangle:
4 m, 5 m, 6 m
29 in, 20 in, 21 in
Cannot Be the Sides of a Right Triangle:
63 in, 16 in, 21 in
Could Be the Sides of a Right Triangle:
- 4 m, 5 m, 6 m
Cannot Be the Sides of a Right Triangle:
- 29 in, 20 in, 21 in
- 63 in, 16 in, 21 in
To determine whether a set of measurements can describe the lengths of the three 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 is equal to the sum of the squares of the lengths of the other two sides.
Let's go through each set of measurements and test if they satisfy the Pythagorean theorem.
1. 4 m, 5 m, 6 m:
To check if these measurements can describe the lengths of the sides of a right triangle, we need to apply the Pythagorean theorem:
c² = a² + b²
(6 m)² = (4 m)² + (5 m)²
36 m² = 16 m² + 25 m²
36 m² ≠ 41 m²
Since the equation is not satisfied, this set of measurements cannot describe the lengths of the sides of a right triangle.
2. 29 in, 20 in, 21 in:
Applying the Pythagorean theorem:
c² = a² + b²
(29 in)² = (20 in)² + (21 in)²
841 in² = 400 in² + 441 in²
841 in² = 841 in²
In this case, the equation is satisfied, which means these measurements can describe the lengths of the sides of a right triangle.
3. 63 in, 16 in, 21 in:
Using the Pythagorean theorem:
c² = a² + b²
(63 in)² = (16 in)² + (21 in)²
3969 in² = 256 in² + 441 in²
3969 in² ≠ 697 in²
Again, the equation is not satisfied, so this set of measurements cannot describe the lengths of the sides of a right triangle.
Therefore, the set of measurements that can describe the lengths of the sides of a right triangle is: 29 in, 20 in, 21 in.
Drag and drop the sets of measurements into the correct boxes:
Could Be the Sides of a Right Triangle: 29 in, 20 in, 21 in
Cannot Be the Sides of a Right Triangle: 4 m, 5 m, 6 m; 63 in, 16 in, 21 in