Question
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)
3
5
3
5
Answers
GPT-4o mini
To find the value of \( x \) as the shortest leg of a right triangle using the geometric mean, we can use the formula that relates the legs of a right triangle and the altitude drawn from the right angle to the hypotenuse.
In this case, if we assume that the two legs of the right triangle are 3 and 5, the geometric mean \( x \) can be found using the formula:
\[
x = \sqrt{a \cdot b}
\]
where \( a = 3 \) and \( b = 5 \).
Calculating this:
\[
x = \sqrt{3 \cdot 5} = \sqrt{15}
\]
Now we will find the approximate decimal value of \( \sqrt{15} \):
\[
\sqrt{15} \approx 3.872
\]
Rounding this to the nearest tenth, we get:
\[
x \approx 3.9
\]
Thus, the value of \( x \) is approximately **3.9**.
In this case, if we assume that the two legs of the right triangle are 3 and 5, the geometric mean \( x \) can be found using the formula:
\[
x = \sqrt{a \cdot b}
\]
where \( a = 3 \) and \( b = 5 \).
Calculating this:
\[
x = \sqrt{3 \cdot 5} = \sqrt{15}
\]
Now we will find the approximate decimal value of \( \sqrt{15} \):
\[
\sqrt{15} \approx 3.872
\]
Rounding this to the nearest tenth, we get:
\[
x \approx 3.9
\]
Thus, the value of \( x \) is approximately **3.9**.