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If the equation

is found to
be true, what do we know
about the triangle?
18^2 + b^2 = 30^2
The triangle is a right
triangle with a missing
side of 34.99.
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, and the legs
are 30 and 24.

1 answer

To solve the equation \( 18^2 + b^2 = 30^2 \), we first calculate both sides.

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

    • \( 18^2 = 324 \)
    • \( 30^2 = 900 \)

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

  3. Solve for \( b^2 \): \[ b^2 = 900 - 324 \] \[ b^2 = 576 \]

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

Thus, we find that the missing side \( b \) is 24.

Now, we evaluate the provided options:

  • The triangle is a right triangle with a missing side of 34.99. (Incorrect)
  • The triangle is a right triangle, and the hypotenuse is 18. (Incorrect; 30 is the hypotenuse)
  • The triangle is a right triangle with a missing leg length of 24. (Correct)
  • The triangle is a right triangle, and the legs are 30 and 24. (Incorrect; 30 is the hypotenuse, not a leg)

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