If the equation 18^2 + b^ = 30^2

Question

is found to be true, what do we know about the triangle?(1 point)
Responses

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

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 legs are 30 and 24.

Answer 1

Let's analyze the equation \(18^2 + b^2 = 30^2\).

1. Calculate \(18^2\): \[ 18^2 = 324 \]

2. Calculate \(30^2\): \[ 30^2 = 900 \]

3. Substitute these values into the equation: \[ 324 + b^2 = 900 \]

4. To find \(b^2\), subtract 324 from both sides: \[ b^2 = 900 - 324 = 576 \]

5. Now take the square root of both sides to find \(b\): \[ b = \sqrt{576} = 24 \]

Since we have \(b = 24\), the equation confirms that the triangle is indeed a right triangle. The lengths of the legs are 18 and 24, with 30 being the hypotenuse.

Therefore, the correct response is:

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