Question

PLS HELP 100 points

A photographic negative is 5.4 cm by 1.35 cm. If you are going to enlarge the image on a 10.2 in by 2.4 in piece of photo paper, what is the largest length and width you can use to keep the photo in proportion to its negative?

Answer 1

Explanation:

To keep the photo in proportion to its negative, you need to maintain the same aspect ratio, which is the ratio of the width to the height of the image. The aspect ratio of the negative is 5.4 cm / 1.35 cm = 4. To maintain this aspect ratio, the aspect ratio of the enlargement must also be 4.

The aspect ratio of the photo paper is 10.2 in / 2.4 in = 4.25. So, the largest length and width that you can use to keep the photo in proportion to its negative is 2.4 in * 4 = 9.6 in and 9.6 in / 4 = 2.4 in, respectively.

Answer 2

• Length = 9.6 in
• Width = 2.4 in

Explanation:

Conversion

• 1 inch ≈ 2.54 cm

First convert the dimensions of the photo paper to centimeters:

`\implies \sf 10.2\;in=10.2 * 2.54=25.908\;cm`

`\implies \sf 2.4\;in=2.4 * 2.54=6.096\;cm`

Therefore, the dimensions of the photo paper in centimeters are:

• 25.908 × 6.096 cm (nearest thousandth)

To determine the dimensions of the photo if the image is enlarged to fit on a 25.908 × 6.096 cm piece of photo paper, first calculate the scale factor by dividing the shortest side of the photo paper by the shortest side of the negative:

`\sf Scale\;factor=(6.096)/(1.35)=4.51555...`

Multiply this scale factor by the longest side of the negative to determine the proportional length of the photo:

`\implies \sf 4.51555...* 5.4=24.384\;cm`

As 24.384 cm is less than the longest side of the photo paper, this scale factor will work to keep the photo in proportion to its negative.

Therefore, the largest length and width you can use to keep the photo in proportion to its negative is:

• 24.384 × 6.096 cm
• 9.6 × 2.4 in