Question

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

A) 65,16,63
B)29,21,20
C) 5,6,4

Answer 1

To determine whether the given sets of measurements can describe the lengths of the three sides of a right triangle, we can use the Pythagorean theorem, which states that for a right triangle with sides \(a\), \(b\), and hypotenuse \(c\):

\[ a^2 + b^2 = c^2 \]

Let's analyze each set of measurements:

**A) 65, 16, 63**
- Largest number (hypotenuse) is 65.
- Check if \(16^2 + 63^2 = 65^2\):
- \(16^2 = 256\)
- \(63^2 = 3969\)
- \(65^2 = 4225\)
- \(256 + 3969 = 4225\)
- **This satisfies the condition.**

**B) 29, 21, 20**
- Largest number (hypotenuse) is 29.
- Check if \(20^2 + 21^2 = 29^2\):
- \(20^2 = 400\)
- \(21^2 = 441\)
- \(29^2 = 841\)
- \(400 + 441 = 841\)
- **This satisfies the condition.**

**C) 5, 6, 4**
- Largest number (hypotenuse) is 6.
- Check if \(4^2 + 5^2 = 6^2\):
- \(4^2 = 16\)
- \(5^2 = 25\)
- \(6^2 = 36\)
- \(16 + 25 = 41\) (which is not equal to 36)
- **This does not satisfy the condition.**

### Now we can organize the responses:

**Could Be the Sides of a Right Triangle:**
- A) 65, 16, 63
- B) 29, 21, 20

**Cannot Be the Sides of a Right Triangle:**
- C) 5, 6, 4