Question

Ella’s geometry teacher asked each student to devise a problem and write out its solution. Here is Ella’s work:

A triangle has side lengths of 10, 11, and 15. What type of triangle is it?

Procedure:

102 ?? 112 + 152

100 ?? 121 + 225

100 < 346

Conclusion:

This triangle is an acute triangle.

Which statement best summarizes Ella’s work?

Ella’s procedure and conclusion are correct.
Ella’s procedure is correct, but her conclusion is incorrect.
Ella’s procedure is incorrect, but her conclusion is correct.
Ella’s procedure and conclusion are incorrect.

Answer 1

D.

Explanation:

Answer 2

Ella’s procedure and conclusion are incorrect.

Explanation:

The sum of the squares of the short sides can be compared to the square of the long side to see if the triangle is acute, right, or obtuse. The appropriate conclusions are ...

• a² +b² > c² -- acute triangle
• a² +b² = c² -- right triangle
• a² +b² < c² -- obtuse triangle

For Ella's side lengths, the appropriate "work" is ...

10² +11² ?? 15²

100 +121 < 225

The triangle is obtuse.

__

Ella used an incorrect comparison and came to the wrong conclusion. Both her procedure and conclusion are incorrect.