Answer:
Alice should pick the size 8-inch by 10-inch ⇒ 2nd choice
Step-by-step explanation:
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
