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)ResponsesNo, 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.

Answer 1

To determine whether a triangle with side lengths 6, 10, and 8 is a right triangle, you would use the Pythagorean theorem. A triangle is a right triangle if \( a^2 + b^2 = c^2 \), where \( c \) is the length of the longest side.

In this case:
- The sides are 6, 8, and 10. The longest side \( c \) is 10.

Now, you calculate:
- \( 6^2 + 8^2 \)
- \( 10^2 \)

Calculating these gives:
- \( 6^2 = 36 \)
- \( 8^2 = 64 \)
- \( 10^2 = 100 \)

Now sum \( 6^2 + 8^2 \):
- \( 36 + 64 = 100 \)

Since \( 100 = 100 \), this means that the triangle with sides 6, 8, and 10 does form a right triangle.

Elinor's calculations were incorrect. She mistakenly compared the squares while not setting the longest side correctly as \( c \). Hence, the correct response is:

No, she should've added \( 6^2 \) and \( 8^2 \) and compared that to \( 10^2 \).