Bianca makes a scale drawing of a rectangular garden. The length is 9 in., and the width is 6 in. Bianca changes the scale of the drawing from 1 in. : 3 ft to 1 in. : 4 ft. Which statement about the dimensions of the garden is true?

Question

The width of the garden under the new scale is 24 ft.
The length of the garden under the new scale is 12 ft.
The length of the garden under the old scale is 36 ft.
The width of the garden under the old scale is 27 ft.

Answer 1

Let's analyze the scale drawings and the conversions to determine the correct statements.

1. Old Scale: 1 in. : 3 ft

• Length of the drawing = 9 in.
• Width of the drawing = 6 in.

Using the old scale:

• Length of the actual garden = 9 in. * 3 ft/in. = 27 ft
• Width of the actual garden = 6 in. * 3 ft/in. = 18 ft

2. New Scale: 1 in. : 4 ft

• Length of the drawing = 9 in.
• Width of the drawing = 6 in.

Using the new scale:

• Length of the actual garden = 9 in. * 4 ft/in. = 36 ft
• Width of the actual garden = 6 in. * 4 ft/in. = 24 ft

Now, let's review the statements:

1. The width of the garden under the new scale is 24 ft. - This is true.
2. The length of the garden under the new scale is 12 ft. - This is false; it is 36 ft.
3. The length of the garden under the old scale is 36 ft. - This is false; it is 27 ft.
4. The width of the garden under the old scale is 27 ft. - This is false; it is 18 ft.

The correct statement is: The width of the garden under the new scale is 24 ft.