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

Question

Responses

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.
No, because 193 does not equal 100.

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

Yes, because it looks like a right triangle.

Answer 1

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

Here, the sides are 7, 10, and 12. The longest side is 12.

We calculate:

1. Square of the longest side: \( 12^2 = 144 \)
2. Sum of the squares of the other two sides: \( 7^2 + 10^2 = 49 + 100 = 149 \)

Now, we compare \( 12^2 \) and \( 7^2 + 10^2 \):

• \( 144 \) (hypotenuse) ≠ \( 149 \) (sum of squares)

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

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