Question
Use the geometric mean to find x, Round your answer to the nearest tenth.
Imagine an isosceles triangle. The top point is leaned to the right. There is a straight line from that point connected to the bottom. On the right side of the triangle thats divided from the left, "3" is under it, and on the left is "6". The line inside the triangle is labelled "x"
Imagine an isosceles triangle. The top point is leaned to the right. There is a straight line from that point connected to the bottom. On the right side of the triangle thats divided from the left, "3" is under it, and on the left is "6". The line inside the triangle is labelled "x"
Answers
GPT-4o mini
In the context of an isosceles triangle as you've described, where there are segments of lengths 3 and 6 on either side of the altitude (or median), we can use the geometric mean to solve for \( x \).
The relationship given by the geometric mean in this case can be expressed as follows:
\[
x^2 = 3 \times 6
\]
Calculating the right side:
\[
x^2 = 18
\]
Now, we take the square root to find \( x \):
\[
x = \sqrt{18}
\]
Simplifying \( \sqrt{18} \):
\[
x = \sqrt{9 \times 2} = 3\sqrt{2} \approx 3 \times 1.414 = 4.242
\]
Rounding to the nearest tenth gives:
\[
x \approx 4.2
\]
So, \( x \) rounded to the nearest tenth is **4.2**.
The relationship given by the geometric mean in this case can be expressed as follows:
\[
x^2 = 3 \times 6
\]
Calculating the right side:
\[
x^2 = 18
\]
Now, we take the square root to find \( x \):
\[
x = \sqrt{18}
\]
Simplifying \( \sqrt{18} \):
\[
x = \sqrt{9 \times 2} = 3\sqrt{2} \approx 3 \times 1.414 = 4.242
\]
Rounding to the nearest tenth gives:
\[
x \approx 4.2
\]
So, \( x \) rounded to the nearest tenth is **4.2**.