Answer :

To determine if [tex]\( x \)[/tex] is 6 in the given proportion [tex]\( 9 : x = x : 4 \)[/tex], we will solve the proportion using cross-multiplication.

1. Set up the proportion equation from the given ratio:
[tex]\[
\frac{9}{x} = \frac{x}{4}
\][/tex]

2. Use cross-multiplication to solve the equation. This means multiplying the means (inside terms) and the extremes (outside terms):
[tex]\[
9 \times 4 = x \times x
\][/tex]

3. Simplify the cross-multiplication:
[tex]\[
36 = x^2
\][/tex]

4. Solve for [tex]\( x \)[/tex] by finding the square root of both sides:
[tex]\[
x = \sqrt{36}
\][/tex]

5. The square root of 36 is 6, so:
[tex]\[
x = 6
\][/tex]

Therefore, the statement "If [tex]\( 9 : x = x : 4 \)[/tex], then [tex]\( x \)[/tex] is 6" is True.

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