Question

1. a photograph is 5 inches by 7 inches. ellie is using a copier to enlarge the photograph. at the 100% setting, the scale factor is 1 . at the 150% setting, the scale factor is 1.5 . she wants to enlarge the photograph as much as possible and still have it fit on an 8.5 by 11 inch piece of paper. which setting would be best?a) 50%b) 125%c) 155%d) 170%11. the aspect ratio of an image is the ratio of the width to the height. the photo of a turtle is enlarged in a manner so that the aspect ratio stays the same.a. what is the aspect ratio of the photo?b. what is the width of the enlarged photo? how do you know?c. how many times longer is the width of the enlarged photo than the width of the original photo?d. explain the similarities and differences between the aspect ratio and the scale factor.

Explanation:

Problem 10

Step1: Calculate max scale for width

$\text{Scale factor (width)} = \frac{8.5}{5} = 1.7 \ (\text{170%})$

Step2: Calculate max scale for height

$\text{Scale factor (height)} = \frac{11}{7} \approx 1.571 \ (\text{157.1%})$

Step3: Choose largest valid setting

The height limits the scale; the largest option ≤157.1% is 155%.

Part a: Find aspect ratio

Step1: Define aspect ratio

$\text{Aspect Ratio} = \frac{\text{Width}}{\text{Height}}$

Step2: Substitute original dimensions

$\text{Aspect Ratio} = \frac{10.64}{8} = 1.33$ or $\frac{133}{100}$
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Part b: Find enlarged width

Step1: Identify scale factor

$\text{Scale Factor} = \frac{\text{Enlarged Height}}{\text{Original Height}} = \frac{12}{8} = 1.5$

Step2: Calculate enlarged width

$\text{Enlarged Width} = 10.64 \times 1.5 = 15.96 \ \text{cm}$
(Aspect ratio is preserved, so width scales by the same factor as height.)
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Part c: Compare widths

Step1: Use scale factor

The scale factor for height (1.5) applies to width, since aspect ratio is constant.
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Part d: Compare aspect ratio/scale factor

Step1: Define key differences/similarities

Aspect ratio is a fixed ratio of an image's own width to height, while scale factor is a multiplier that resizes the entire image relative to its original dimensions. Both relate to proportionality, but aspect ratio describes the image's shape, and scale factor describes its size change.

Answer:

C) 155%

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Problem 11