Question
The rectangle on the right is a scaled copy of the rectangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
the left one has a 14 on top with a on the side and the right one has a 7 not he and a 3 on the bottom
the left one has a 14 on top with a on the side and the right one has a 7 not he and a 3 on the bottom
Answers
Answered by
GPT-4o mini
To find the scale factor of the rectangles, we can use the dimensions given.
The rectangle on the left has a width of 14 and a height (not specified but represented as a blank) and the rectangle on the right has a width of 7 and a height of 3.
If we assume the rectangular dimensions are as follows:
- Left rectangle: Width = 14 and Height = H (unspecified)
- Right rectangle: Width = 7 and Height = 3
To find the scale factor for the width, we compare the widths of the two rectangles:
\[
\text{Scale Factor} = \frac{\text{Width of the right rectangle}}{\text{Width of the left rectangle}} = \frac{7}{14} = \frac{1}{2}
\]
To determine the scale factor for the height, we need the height H of the left rectangle. If we had the height of the left rectangle, we would find:
\[
\text{Scale Factor for height} = \frac{\text{Height of the right rectangle}}{\text{Height of the left rectangle}} = \frac{3}{H}
\]
Since the problem states that the rectangles are scaled copies, the heights must also be proportional.
Given the width scale factor is \( \frac{1}{2} \), if the left rectangle's height is double that of the right rectangle, then:
- If \( H = 6 \) (for example), we would have:
\[
\frac{3}{6} = \frac{1}{2}
\]
Thus, the scale factor for both dimensions would be \( \frac{1}{2} \). However, without the specific height of the left rectangle, we assume the height is compatible with this scale factor.
From the information provided, the scale factor is \( \frac{1}{2} \).
The rectangle on the left has a width of 14 and a height (not specified but represented as a blank) and the rectangle on the right has a width of 7 and a height of 3.
If we assume the rectangular dimensions are as follows:
- Left rectangle: Width = 14 and Height = H (unspecified)
- Right rectangle: Width = 7 and Height = 3
To find the scale factor for the width, we compare the widths of the two rectangles:
\[
\text{Scale Factor} = \frac{\text{Width of the right rectangle}}{\text{Width of the left rectangle}} = \frac{7}{14} = \frac{1}{2}
\]
To determine the scale factor for the height, we need the height H of the left rectangle. If we had the height of the left rectangle, we would find:
\[
\text{Scale Factor for height} = \frac{\text{Height of the right rectangle}}{\text{Height of the left rectangle}} = \frac{3}{H}
\]
Since the problem states that the rectangles are scaled copies, the heights must also be proportional.
Given the width scale factor is \( \frac{1}{2} \), if the left rectangle's height is double that of the right rectangle, then:
- If \( H = 6 \) (for example), we would have:
\[
\frac{3}{6} = \frac{1}{2}
\]
Thus, the scale factor for both dimensions would be \( \frac{1}{2} \). However, without the specific height of the left rectangle, we assume the height is compatible with this scale factor.
From the information provided, the scale factor is \( \frac{1}{2} \).