Question

consider the enlargement of the triangle. which proportional statements are true for finding the value of x? check all that apply.
$\frac{x}{16}=\frac{9}{6}$
$\frac{x}{6}=\frac{9}{16}$
$\frac{6}{16}=\frac{9}{x}$
$\frac{16}{x}=\frac{6}{9}$
$\frac{x}{16}=\frac{6}{9}$

Explanation:

Step1: Use the property of similar triangles

For similar triangles, the ratios of corresponding sides are equal.

Step2: Analyze each proportion

• For \(\frac{x}{16}=\frac{9}{6}\), cross - multiply: \(6x = 16\times9\), \(x=\frac{16\times9}{6}=24\).
• For \(\frac{x}{6}=\frac{9}{16}\), cross - multiply: \(16x=6\times9\), \(x = \frac{6\times9}{16}=\frac{27}{8}\).
• For \(\frac{6}{16}=\frac{9}{x}\), cross - multiply: \(6x=16\times9\), \(x = 24\).
• For \(\frac{16}{x}=\frac{6}{9}\), cross - multiply: \(6x=16\times9\), \(x = 24\).
• For \(\frac{x}{16}=\frac{6}{9}\), cross - multiply: \(9x=16\times6\), \(x=\frac{16\times6}{9}=\frac{32}{3}\).

Answer:

\(\frac{x}{16}=\frac{9}{6}\), \(\frac{6}{16}=\frac{9}{x}\), \(\frac{16}{x}=\frac{6}{9}\)