Question

solving scale problems using proportions
writing proportions
consider the enlargement of the rectangle.
which proportional statements are true of the
enlargement? choose three correct answers.
\\( \frac { \text { width original } } { \text { length original } } = \frac { \text { width enlargement } } { \text { length enlargement } } \\)
\\( \frac { \text { width original } } { \text { length enlargement } } = \frac { \text { width enlargement } } { \text { length original } } \\)
\\( \frac { \text { width enlargement } } { \text { length enlargement } } = \frac { \text { width original } } { \text { length original } } \\)
\\( \frac { \text { length original } } { \text { width enlargement } } = \frac { \text { length enlargement } } { \text { width original } } \\)

Explanation:

Step1: Analyze the first proportion

For the proportion \(\frac{\text{width original}}{\text{length original}}=\frac{\text{width enlargement}}{\text{length enlargement}}\), cross - multiply gives \(\text{width original}\times\text{length enlargement}=\text{width enlargement}\times\text{length original}\). Substituting the values: original width \(w_1 = 6\), original length \(l_1=12\), enlargement width \(w_2 = 2\), enlargement length \(l_2 = 4\). We get \(6\times4=2\times12\), \(24 = 24\).

Step2: Analyze the second proportion

For the proportion \(\frac{\text{length enlargement}}{\text{width original}}=\frac{\text{width enlargement}}{\text{length original}}\), cross - multiply gives \(\text{length enlargement}\times\text{length original}=\text{width enlargement}\times\text{width original}\). Substituting the values: \(4\times12=2\times6\), \(48
eq12\).

Step3: Analyze the third proportion

For the proportion \(\frac{\text{length enlargement}}{\text{width enlargement}}=\frac{\text{length original}}{\text{width original}}\), cross - multiply gives \(\text{length enlargement}\times\text{width original}=\text{width enlargement}\times\text{length original}\). Substituting the values: \(4\times6=2\times12\), \(24 = 24\).

Step4: Analyze the fourth proportion

For the proportion \(\frac{\text{width enlargement}}{\text{length original}}=\frac{\text{width original}}{\text{length enlargement}}\), cross - multiply gives \(\text{width enlargement}\times\text{length enlargement}=\text{width original}\times\text{length original}\). Substituting the values: \(2\times4=6\times12\), \(8
eq72\).

Answer:

The first and the third proportions are correct.