Question

sid was given the following enlargement of a rectangle.
sid calculated the scale factor to be \\( \frac { 1 } { 5 } \\). what error, if any, did sid make when he calculated the scale factor?
\\( \bigcirc \\) sid found the reciprocal of the scale factor.
\\( \bigcirc \\) sid used the wrong dimensions to calculate the scale factor. he should have gotten \\( \frac { 5 } { 2 } \\) as the scale factor.
\\( \bigcirc \\) sid used the wrong dimensions to calculate the scale factor. he should have gotten \\( \frac { 2 } { 5 } \\) as the scale factor.
\\( \bigcirc \\) sid did not make an error calculating the scale factor. the correct scale factor is \\( \frac { 1 } { 5 } \\).

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) for an enlargement is given by \(k=\frac{\text{new dimension}}{\text{original dimension}}\).

Step2: Identify the correct dimensions

The original rectangle has a width of \(4\) ft and the new (enlarged) rectangle has a width of \(20\) ft.

Step3: Calculate the correct scale factor

Using the formula \(k = \frac{20}{4}=5\).

Step4: Analyze Sid's error

Sid used the height of the original rectangle (\(8\) ft) and the width of the new rectangle (\(20\) ft). He should have used the corresponding dimensions (either both widths or both heights). For example, if we use heights: original height \(h_1 = 8\) ft, new height \(h_2\). Since the scale factor \(k = 5\), then \(h_2=8\times5 = 40\) ft. The error is that Sid used non - corresponding dimensions (height of original and width of new) to calculate the scale factor.

Answer:

Sid used the wrong dimensions to calculate the scale factor. He should have used either both widths (original width \(4\) ft and new width \(20\) ft) or both heights (if we assume the height of the new rectangle is \(40\) ft as per scale factor \(k = 5\) from width calculation). So the answer is "Sid used the wrong dimensions to calculate the scale factor. He should have used either both widths or both heights".