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Question

Question
Can a triangle with sides 7, 10, and 12 be a right triangle? How do you know?(1 point)
Responses

Yes, because it looks like a right triangle.
Yes, because it looks like a right triangle.
There is no way to tell without an angle measure.
There is no way to tell without an angle measure.
No, because 149 does not equal 144.
No, because 149 does not equal 144.
No, because 193 does not equal 100.

Answer 1

To determine if a triangle with sides 7, 10, and 12 can be a right triangle, we can use the Pythagorean theorem. According to the theorem, for a triangle to be a right triangle, the square of the length of the longest side (hypotenuse) must equal the sum of the squares of the other two sides.

In this case, let’s check:

1. Identify the longest side: Here, 12 is the longest side.

2. Calculate the squares of the sides:

   • 7² = 49
   • 10² = 100
   • 12² = 144

3. Now, check if 12² = 7² + 10²:

   • 144 = 49 + 100
   • 144 = 149 (this is incorrect)

Since 144 does not equal 149, the triangle with sides 7, 10, and 12 cannot be a right triangle.

The correct answer is: No, because 149 does not equal 144.