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Question

A line, x, divides a right triangle from the vertex opposite the hypotenuse to the hypotenuse. The line x forms a second right angle, marked by a small square, where it meets the hypotenuse, and it divides the hypotenuse into 6 and 3.

Use the geometric mean to find x. Round your answer to the nearest tenth.

(1 point)

Answer 1

To find the length of the line \( x \) using the geometric mean, we can use the property of right triangles that states if a line is drawn from the vertex of the right angle to the hypotenuse, the length of that line is the geometric mean of the lengths of the two segments it creates on the hypotenuse.

In this case, the hypotenuse is divided into two segments of lengths 6 and 3.

The geometric mean \( x \) can be calculated using the formula:

\[ x = \sqrt{(6)(3)} \]

Now, calculate \( x \):

\[ x = \sqrt{18} \]

Calculating the square root:

\[ x \approx 4.2426 \]

Rounding to the nearest tenth:

\[ x \approx 4.2 \]

Thus, the length of the line \( x \) is approximately 4.2.