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

Question

18
2

+

𝑏
2

=

30
2
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

The equation \( 18^2 + b^2 = 30^2 \) represents a right triangle based on the Pythagorean theorem, where \( a^2 + b^2 = c^2 \) for a triangle with legs \( a \) and \( b \), and hypotenuse \( c \).

In this case:

• \( a = 18 \)
• \( c = 30 \)

To find \( b \), we can rearrange the equation:

\[ b^2 = 30^2 - 18^2 \] \[ b^2 = 900 - 324 \] \[ b^2 = 576 \] \[ b = \sqrt{576} \] \[ b = 24 \]

Thus, the missing leg length is 24. Therefore, the correct response is:

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