Question
Elinor determined that a triangle with side lengths 6, 10, and 8 does not form a right triangle using the following steps:
62+102=82
36+100=64
136≠64
Is her answer correct?
(1 point)
Responses
No, she should've added 102
and 82
and compared that to 62
.
No, she should've added 10 squared and 8 squared and compared that to 6 squared.
No, she should've added 62
and 82
and compared that to 102
.
No, she should've added 6 squared and 8 squared and compared that to 10 squared.
Yes, she is correct.
Yes, she is correct.
No, she should've added 62
from 102
and compared that to 82
.
62+102=82
36+100=64
136≠64
Is her answer correct?
(1 point)
Responses
No, she should've added 102
and 82
and compared that to 62
.
No, she should've added 10 squared and 8 squared and compared that to 6 squared.
No, she should've added 62
and 82
and compared that to 102
.
No, she should've added 6 squared and 8 squared and compared that to 10 squared.
Yes, she is correct.
Yes, she is correct.
No, she should've added 62
from 102
and compared that to 82
.
Answers
GPT-4o mini
To determine whether the triangle with side lengths 6, 10, and 8 is a right triangle, we can apply the Pythagorean theorem, which states that for a triangle to be a right triangle, the sum of the squares of the two shorter sides must equal the square of the longest side.
In this case, the sides are:
- \( a = 6 \)
- \( b = 8 \)
- \( c = 10 \) (the longest side)
We check if \( a^2 + b^2 = c^2 \):
1. Calculate \( a^2 \):
\( 6^2 = 36 \)
2. Calculate \( b^2 \):
\( 8^2 = 64 \)
3. Calculate \( c^2 \):
\( 10^2 = 100 \)
Now add \( a^2 \) and \( b^2 \):
\( 36 + 64 = 100 \)
Since \( 100 = 100 \), the condition holds true. Therefore, the triangle with side lengths 6, 10, and 8 **does** form a right triangle.
Elinor's calculations were incorrect because she did not compare \( 6^2 \) and \( 8^2 \) to \( 10^2 \) directly.
Thus, the correct response is:
**No, she should've added \( 6^2 \) and \( 8^2 \) and compared that to \( 10^2 \).**
In this case, the sides are:
- \( a = 6 \)
- \( b = 8 \)
- \( c = 10 \) (the longest side)
We check if \( a^2 + b^2 = c^2 \):
1. Calculate \( a^2 \):
\( 6^2 = 36 \)
2. Calculate \( b^2 \):
\( 8^2 = 64 \)
3. Calculate \( c^2 \):
\( 10^2 = 100 \)
Now add \( a^2 \) and \( b^2 \):
\( 36 + 64 = 100 \)
Since \( 100 = 100 \), the condition holds true. Therefore, the triangle with side lengths 6, 10, and 8 **does** form a right triangle.
Elinor's calculations were incorrect because she did not compare \( 6^2 \) and \( 8^2 \) to \( 10^2 \) directly.
Thus, the correct response is:
**No, she should've added \( 6^2 \) and \( 8^2 \) and compared that to \( 10^2 \).**