Rasheeda sees a garden in a book. She changes the scale because she wants a garden with different dimensions. The figure below shows both scales and a scale drawing of the garden.

Question

Book scale: 1 inch = 2 feet. Rasheeda's Scale: 2 inches = 3 feet. A rectangle with length A of 18 inches and width B of 6 inches.

Which statements about the gardens are true? Select three options.
Length A of the book’s garden is 18 ft.
Length A of Rasheeda’s garden is 27 ft.
Length B of the book’s garden is 12 ft.
Length B of Rasheeda’s garden is 6 ft.
Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.
Length B of the book’s garden is 3 ft shorter than length B of Rasheeda’s garden.

Answer 1

To make accurate comparisons between the gardens based on their respective scales, we will first convert the dimensions of both gardens according to the scales given.

1. Book Scale: 1 inch = 2 feet

   • Length A in the book: 18 inches
     • Conversion: 18 inches * 2 feet/inch = 36 feet
   • Width B in the book: 6 inches
     • Conversion: 6 inches * 2 feet/inch = 12 feet

2. Rasheeda's Scale: 2 inches = 3 feet

   • We can convert Rasheeda's dimensions back into feet using the same concept.
   • Length A in Rasheeda's garden: 18 inches
     • Conversion: \[ \frac{18 \text{ inches}}{2 \text{ inches}} \times 3 \text{ feet} = 27 \text{ feet} \]
   • Width B in Rasheeda's garden: 6 inches
     • Conversion: \[ \frac{6 \text{ inches}}{2 \text{ inches}} \times 3 \text{ feet} = 9 \text{ feet} \]

Now, let's summarize the dimensions:

• Length A of the book's garden: 36 feet
• Width B of the book's garden: 12 feet
• Length A of Rasheeda’s garden: 27 feet
• Width B of Rasheeda's garden: 9 feet

Now let’s evaluate each statement:

1. Length A of the book’s garden is 18 ft. - False (It's actually 36 feet).
2. Length A of Rasheeda’s garden is 27 ft. - True.
3. Length B of the book’s garden is 12 ft. - True.
4. Length B of Rasheeda’s garden is 6 ft. - False (It's actually 9 feet).
5. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden. - False (36 feet - 27 feet = 9 feet difference, but it's not accurate to say "9 ft longer").
6. Length B of the book’s garden is 3 ft shorter than length B of Rasheeda’s garden. - True (12 feet - 9 feet = 3 feet shorter).

The three true statements are:

• Length A of Rasheeda’s garden is 27 ft.
• Length B of the book’s garden is 12 ft.
• Length B of the book’s garden is 3 ft shorter than length B of Rasheeda’s garden.