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. Show your work.(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 Skip to navigation the respones are [4m 5m 6m] [63 in 16 in 65 in] [29 in 20 in 21 in]

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. The theorem states that for a triangle with sides of lengths \(a\), \(b\), and \(c\) (where \(c\) is the longest side), the following must hold true:

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

Let's analyze each set of measurements:

1. [4m, 5m, 6m]

   • Identify the longest side: 6m
   • Check if \(6^2 = 4^2 + 5^2\): \[ 36 = 16 + 25 \implies 36 = 41 \text{ (False)} \]
   • Conclusion: Cannot be the sides of a right triangle.

2. [63 in, 16 in, 65 in]

   • Identify the longest side: 65 in
   • Check if \(65^2 = 63^2 + 16^2\): \[ 4225 = 3969 + 256 \implies 4225 = 4225 \text{ (True)} \]
   • Conclusion: Could be the sides of a right triangle.

3. [29 in, 20 in, 21 in]

   • Identify the longest side: 29 in
   • Check if \(29^2 = 20^2 + 21^2\): \[ 841 = 400 + 441 \implies 841 = 841 \text{ (True)} \]
   • Conclusion: Could be the sides of a right triangle.

Summary of Results:

• Could Be the Sides of a Right Triangle: [63 in, 16 in, 65 in], [29 in, 20 in, 21 in]
• Cannot Be the Sides of a Right Triangle: [4m, 5m, 6m]