Pythagorean Theorem Proofs Quick Check

Question

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Question
If the equation 182 + b2 = 302 is found to be true, what do we know about the triangle?(1 point)
Responses

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 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 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.

Answer 1

To analyze the equation \( 18^2 + b^2 = 30^2 \), let's first compute the squares:

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

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

Now, we can substitute these values back into the equation: \[ 324 + b^2 = 900 \]

Next, we can solve for \( b^2 \): \[ b^2 = 900 - 324 \] \[ b^2 = 576 \]

Taking the square root of both sides gives us: \[ b = 24 \]

So the triangle is indeed a right triangle with the leg lengths of 18 and 24, and the hypotenuse of 30.

Thus, the correct response is: The triangle is a right triangle with a missing leg length of 24.