Alice has a 4-inch by 5-inch photo of your school's championship girls' ice hockey team. To celebrate their recent victory, your principal wants Alice to enlarge her photo for a display case near the main office. When Alice went to the print shop, she was confronted with many choices of sizes: 7-inch by 9-inch, 8-inch by 10- inch, and 12-inch by 16-inch.She's afraid that if she picks the wrong size, part of the photo will be cut off. Which size should Alice pick and why?

If a rectangle is enlargement by a scale factor k, then each dimension of the original rectangle is multiplied by k to find the dimensions of the new rectangle after enlargement

∵ Alice has a 4-inch by 5-inch photo

- The photo is shaped a rectangle

∴ The dimensions of the original photo are 4 inches and 5 inches

Assume that she enlarges the photo by scale factor k

Multiply the dimensions of the original photo by k

∵ The dimensions of the new photo are 4 × k and 5 × k

∴ The dimensions of the new photo are 4k and 5k

Let us check which choice is the right size

7-inch by 9-inch

∵ 4k = 7

- Divide both sides by 4

∴ k = 1.75

∵ 5k = 9

- Divide both sides by 5

∴ k = 1.8

- The values of k are not equal

∴ 7-inch by 9-inch is not the right size

8-inch by 10-inch

∵ 4k = 8

- Divide both sides by 4

∴ k = 2

∵ 5k = 10

- Divide both sides by 5

∴ k = 2

- The values of k are equal

∴ 8-inch by 10-inch is the right size

12-inch by 16-inch

∵ 4k = 12

- Divide both sides by 4

∴ k = 3

∵ 5k = 16

- Divide both sides by 5

∴ k = 3.2

- The values of k are not equal

∴ 12-inch by 16-inch is not the right size

Alice should pick the size 8-inch by 10-inch