Question

Question

Use the image to answer the question.

A line divides a right triangle from the vertex opposite the hypotenuse to the hypotenuse.

Use the geometric mean to find the value of x, which is the shortest leg of the large triangle. Round to the nearest tenth, if necessary.

(1 point)
Responses

15
15

2.8
2.8

8
8

4.9
4.9
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Answer 1

To find the value of \( x \) using the geometric mean in a right triangle, we can apply the geometric mean theorem. This theorem states that in a right triangle, the altitude to the hypotenuse creates two smaller right triangles that are similar to the original triangle and to each other.

According to the theorem:

\[ x^2 = a \cdot b \]

where:

• \( x \) is the length of the altitude from the vertex opposite the hypotenuse to the hypotenuse,
• \( a \) and \( b \) are the lengths of the segments of the hypotenuse created by the foot of the altitude.

To solve for \( x \), we need the values of \( a \) and \( b \), which are the segments of the hypotenuse.

If you provide the lengths of \( a \) and \( b \), I can help you calculate \( x \). Alternatively, if you are looking for a specific answer based on multiple choice options given in your question, please check the values you have for \( a \) and \( b \) and apply the formula, then select the closest answer rounded to the nearest tenth.