Question

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

There is no way to tell without an angle measure.
There is no way to tell without an angle measure.

Yes, because it looks like a right triangle.
Yes, because it looks like a right triangle.

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, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) equals the sum of the squares of the lengths of the other two sides.

Let's label the sides:
- a = 7
- b = 10
- c = 12 (hypotenuse, since it is the longest side)

Now, we check the Pythagorean theorem:

\( c^2 = a^2 + b^2 \)

Calculating each side:
- \( c^2 = 12^2 = 144 \)
- \( a^2 + b^2 = 7^2 + 10^2 = 49 + 100 = 149 \)

Now we compare:
- \( 144 \) (from \( c^2 \)) and \( 149 \) (from \( a^2 + b^2 \))

Since \( 144 \neq 149 \), the triangle cannot be a right triangle.

Therefore, the correct response is:
**No, because 149 does not equal 144.**