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

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 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.
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Answer 1

To determine what the equation \( 18^2 + b^2 = 30^2 \) tells us about the triangle, we can calculate the values:

1. Calculate \( 18^2 \) and \( 30^2 \): \[ 18^2 = 324 \] \[ 30^2 = 900 \]

2. Substitute \( 18^2 \) into the equation: \[ 324 + b^2 = 900 \]

3. Subtract 324 from both sides: \[ b^2 = 900 - 324 \] \[ b^2 = 576 \]

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

So, we find that the missing leg length \( b \) is 24. This means that:

• The triangle is a right triangle.
• The lengths of the legs are 18 and 24, while the hypotenuse is 30.

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