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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

No, because 149 does not equal 144
No, because 149 does not equal 144

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 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 apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

1. Identify the longest side: In this case, the longest side is 12.

2. According to the Pythagorean theorem, we check if:

   \( 12^2 = 7^2 + 10^2 \)

   Calculating each side:

   • \( 12^2 = 144 \)
   • \( 7^2 = 49 \)
   • \( 10^2 = 100 \)
   • Now, add \( 7^2 \) and \( 10^2 \): \( 49 + 100 = 149 \)

Now we compare the two results:

• \( 144 \) (from \( 12^2 \)) does not equal \( 149 \) (from \( 7^2 + 10^2 \)).

Since \( 144 \neq 149 \), the sides 7, 10, and 12 cannot form a right triangle.

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