Question

solving scale problems using proportions
setting up a proportion to find a missing measure
consider the enlargement of the rectangle.
what is the correct multiplication of a cross product to solve
for the missing dimension?

Explanation:

Step1: Set up the proportion

Since the rectangles are similar, the ratios of their corresponding sides are equal. So, \(\frac{12}{5\frac{3}{5}}=\frac{20}{x}\).

Step2: Convert the mixed number to an improper fraction

\(5\frac{3}{5}=\frac{5\times5 + 3}{5}=\frac{28}{5}\). The proportion becomes \(\frac{12}{\frac{28}{5}}=\frac{20}{x}\).

Step3: Simplify the left - hand side of the proportion

\(\frac{12}{\frac{28}{5}}=12\times\frac{5}{28}=\frac{60}{28}=\frac{15}{7}\). So, \(\frac{15}{7}=\frac{20}{x}\).

Step4: Cross - multiply

Cross - multiplying gives \(15x = 20\times7\).

Step5: Solve for \(x\)

\(15x=140\), then \(x=\frac{140}{15}=\frac{28}{3}=9\frac{1}{3}\).

Answer:

\(x = 9\frac{1}{3}\)