Question
Lewis needed to find the difference in lengths between the hypotenuse and the longest leg of this triangle. His work is shown below.
Triangle A B C. Side B C is 16 and side A C is 12. Hypotenuse A B is labeled c.
12 squared + 16 squared = c squared. 144 + 256 = c squared. 400 = c squared. StartRoot 400 EndRoot = c. 200 = c. Difference: 200 minus 12 = 188.
What errors did Lewis make? Check all that apply.
He simplified StartRoot 400 EndRoot incorrectly. It should be 20 instead of 200.
He found the difference between the hypotenuse and the short leg instead of the long leg.
He evaluated 12 squared incorrectly. It should be 12 (2) = 24.
He evaluated 16 squared incorrectly. It should be 16 (2) = 32.
He should not have taken the square root of each side to get rid of the exponent.
Triangle A B C. Side B C is 16 and side A C is 12. Hypotenuse A B is labeled c.
12 squared + 16 squared = c squared. 144 + 256 = c squared. 400 = c squared. StartRoot 400 EndRoot = c. 200 = c. Difference: 200 minus 12 = 188.
What errors did Lewis make? Check all that apply.
He simplified StartRoot 400 EndRoot incorrectly. It should be 20 instead of 200.
He found the difference between the hypotenuse and the short leg instead of the long leg.
He evaluated 12 squared incorrectly. It should be 12 (2) = 24.
He evaluated 16 squared incorrectly. It should be 16 (2) = 32.
He should not have taken the square root of each side to get rid of the exponent.
Answers
GPT-4o mini
Lewis made the following errors:
1. **He simplified StartRoot 400 EndRoot incorrectly. It should be 20 instead of 200.** - This is correct; he incorrectly stated that \(\sqrt{400} = 200\) instead of \(\sqrt{400} = 20\).
2. **He found the difference between the hypotenuse and the short leg instead of the long leg.** - This is also correct; the correct difference should have been between the hypotenuse (20) and the longest leg (16), not the shortest leg (12).
The following statements are incorrect:
3. **He evaluated 12 squared incorrectly. It should be 12 (2) = 24.** - This is incorrect; 12 squared is 144, not 24.
4. **He evaluated 16 squared incorrectly. It should be 16 (2) = 32.** - This is also incorrect; 16 squared is 256, not 32.
5. **He should not have taken the square root of each side to get rid of the exponent.** - This statement is incorrect; he correctly took the square root of both sides when solving for c.
In summary, Lewis made errors in simplifying the square root and in determining which sides to find the difference between.
1. **He simplified StartRoot 400 EndRoot incorrectly. It should be 20 instead of 200.** - This is correct; he incorrectly stated that \(\sqrt{400} = 200\) instead of \(\sqrt{400} = 20\).
2. **He found the difference between the hypotenuse and the short leg instead of the long leg.** - This is also correct; the correct difference should have been between the hypotenuse (20) and the longest leg (16), not the shortest leg (12).
The following statements are incorrect:
3. **He evaluated 12 squared incorrectly. It should be 12 (2) = 24.** - This is incorrect; 12 squared is 144, not 24.
4. **He evaluated 16 squared incorrectly. It should be 16 (2) = 32.** - This is also incorrect; 16 squared is 256, not 32.
5. **He should not have taken the square root of each side to get rid of the exponent.** - This statement is incorrect; he correctly took the square root of both sides when solving for c.
In summary, Lewis made errors in simplifying the square root and in determining which sides to find the difference between.