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. 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

Answer 1

I’m missing the actual sets of measurements you want sorted. Please paste them and I’ll put each set into the correct box and show the work.

Meanwhile, here’s the method I’ll use so you can see how I decide:

1. Check that all three numbers are positive. If any ≤ 0, they cannot be side lengths.
2. Sort the three numbers from smallest to largest: a ≤ b ≤ c.
3. Use the Pythagorean test: if a^2 + b^2 = c^2 (exactly for integers, or within a small tolerance for decimals), then they can be the sides of a right triangle. Put that set in “Could Be the Sides of a Right Triangle.”
4. If a^2 + b^2 ≠ c^2, then they cannot form a right triangle. Put that set in “Cannot Be the Sides of a Right Triangle.”
(Note: If they fail the triangle inequality a + b > c, they also cannot be any triangle; that’s an immediate “Cannot.”)

Examples:
- {3, 4, 5} → sorted 3,4,5. 3^2 + 4^2 = 9 + 16 = 25 = 5^2 → Could be the sides of a right triangle.
- {2, 3, 4} → sorted 2,3,4. 2^2 + 3^2 = 4 + 9 = 13 ≠ 16 = 4^2 → Cannot be the sides of a right triangle.
- {1.5, 2.0, 2.5} → sorted 1.5,2.0,2.5. 1.5^2 + 2.0^2 = 2.25 + 4 = 6.25 = 2.5^2 → Could be the sides of a right triangle.

Send the sets and I’ll sort them into the two boxes and show the arithmetic for each.