Question

1. the two triangles are similar. set up and solve a proportion to find the unknown side length.

\\(\frac{9}{7}\\) yd, \\(\frac{7}{2}\\) yd, 3 yd
options:
\\(s = 1\frac{5}{49}\\)
\\(s = 1\frac{1}{2}\\) yd
\\(s = 1\frac{1}{6}\\)
\\(s = 4\frac{11}{14}\\)

Explanation:

Step1: Set up similarity proportion

$\frac{s}{\frac{7}{2}} = \frac{\frac{9}{7}}{3}$

Step2: Simplify right-hand side

$\frac{s}{\frac{7}{2}} = \frac{9}{7 \times 3} = \frac{3}{7}$

Step3: Solve for $s$

$s = \frac{3}{7} \times \frac{7}{2}$

Step4: Calculate final value

$s = \frac{3}{2} = 1\frac{1}{2}$

Answer:

$s = 1\frac{1}{2}$ yd (matches the second option: $\boldsymbol{s = 1\frac{1}{2}}$ yd)