If the equation 18^2 + b^2 = 30^2 is found to be true, what do we know about the triangle?(1 point)

Question

Responses

The triangle is a right triangle with a missing leg length of 24.
The triangle is a right triangle with a missing leg length of 24.

The triangle is a right triangle, and the hypotenuse is 18.
The triangle is a right triangle, and the hypotenuse is 18.

The triangle is a right triangle, and the legs are 30 and 24.
The triangle is a right triangle, and the legs are 30 and 24.

The triangle is a right triangle with a missing side of 34.99.
The triangle is a right triangle with a missing side of 34.99.

Answer 1

To solve the equation \( 18^2 + b^2 = 30^2 \), we can determine whether it represents a right triangle using the Pythagorean theorem, where \( c \) is the length of the hypotenuse and \( a \) and \( b \) are the lengths of the other two sides.

1. Calculate \( 18^2 \) and \( 30^2 \):

   \( 18^2 = 324 \)

   \( 30^2 = 900 \)

2. Substitute these values into the equation:

   \( 324 + b^2 = 900 \)

3. To find \( b^2 \), rearrange the equation:

   \( b^2 = 900 - 324 \)

   \( b^2 = 576 \)

4. Now, take the square root of both sides to find \( b \):

   \( b = \sqrt{576} = 24 \)

With this information, we conclude that:

The triangle is a right triangle with a missing leg length of 24.