Question

these rectangles are similar. which proportion shows the correct relationship between these two figures? $\frac{30}{12}=\frac{10}{4}$ $\frac{30}{12}=\frac{12}{4}$ $\frac{30}{10}=\frac{30}{12}$ $\frac{4}{12}=\frac{10}{4}$

Explanation:

Step1: Recall the property of similar rectangles

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

Step2: Identify corresponding sides

The side of length \(30\) yd in the larger rectangle corresponds to the side of length \(10\) yd in the smaller rectangle. The side of length \(12\) yd in the larger rectangle corresponds to the side of length \(4\) yd in the smaller rectangle.

Step3: Set up the proportion

The ratio of the longer sides should be equal to the ratio of the shorter sides. So, \(\frac{30}{10}=\frac{12}{4}\), which can be rewritten as \(\frac{30}{12}=\frac{10}{4}\) (by cross - multiplying and rearranging).

Answer:

\(\frac{30}{12}=\frac{10}{4}\) (the first option)