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

Question

Responses

No, because 149 does not equal 144.
No, because 149 does not equal 144. - no response given

Yes, because it looks like a right triangle.
Yes, because it looks like a right triangle. - no response given

No, because 193 does not equal 100.
No, because 193 does not equal 100. - no response given

There is no way to tell without an angle measure.

Answer 1

To determine if a triangle with sides 7, 10, and 12 can be a right triangle, we can use the Pythagorean theorem. The theorem 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 sides: The sides are 7, 10, and 12. The longest side is 12.
2. Apply the Pythagorean theorem:
   • Hypotenuse (c) = 12 → \( c^2 = 12^2 = 144 \)
   • Other sides (a and b) = 7 and 10 → \( a^2 + b^2 = 7^2 + 10^2 = 49 + 100 = 149 \)

Now we compare \( c^2 \) and \( a^2 + b^2 \):

• \( c^2 = 144 \)
• \( a^2 + b^2 = 149 \)

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

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