Question

Use the image to answer the 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 5 and 12.

Use the geometric mean to solve for the value of x.

(1 point)
Responses

2.65
2.65

60
60

7.75
7.75

17

Answer 1

In a right triangle, when a line is drawn from the vertex opposite the hypotenuse to the hypotenuse, and it creates two segments on the hypotenuse (let's call them \( a \) and \( b \)), the length of the line is given by the geometric mean of the two segments into which it divides the hypotenuse.

Given:
- \( a = 5 \)
- \( b = 12 \)

The length \( x \) of the line is calculated using the formula:

\[
x = \sqrt{a \times b}
\]

Substituting in the values:

\[
x = \sqrt{5 \times 12} = \sqrt{60}
\]

Calculating \( \sqrt{60} \):

\[
\sqrt{60} \approx 7.75
\]

Therefore, the value of \( x \) is approximately **7.75**.

So the correct response is:

**7.75**