1 centimeter = 3 meters. A rectangle with length 7 centimeters and width 1.75 centimeters.

Question

Gabriel planned a vegetable garden. Use the scale and the scale drawing to complete the following statements.

The length of the garden is
meters.
The width of the garden is
meters.
If the scale changes to 1 cm : 9 meters, the new length of the garden is
meters and the new width of the garden is
meters.
The new length of the garden is
times as long as the original length of the garden.

Answer 1

The information given about the scale is incorrect: 1 centimeter does not equal 3 meters. Instead, using the conversion correctly, we can say that 1 centimeter = 0.01 meters.

Original Scale (1 cm : 3 m)

1. Length of the garden:

   • Length = 7 cm
   • In meters: \( 7 \text{ cm} \times 3 \text{ m/cm} = 21 \text{ m} \)

2. Width of the garden:

   • Width = 1.75 cm
   • In meters: \( 1.75 \text{ cm} \times 3 \text{ m/cm} = 5.25 \text{ m} \)

New Scale (1 cm : 9 m)

1. New Length of the garden:

   • Length = 7 cm
   • In meters: \( 7 \text{ cm} \times 9 \text{ m/cm} = 63 \text{ m} \)

2. New Width of the garden:

   • Width = 1.75 cm
   • In meters: \( 1.75 \text{ cm} \times 9 \text{ m/cm} = 15.75 \text{ m} \)

Comparison of Lengths

To find out how many times the new length is compared to the original length:

• Original Length = 21 m
• New Length = 63 m
• The factor by which the new length is longer: \[ \frac{63 \text{ m}}{21 \text{ m}} = 3 \]

Summary

• The length of the garden is 21 meters.
• The width of the garden is 5.25 meters.
• If the scale changes to 1 cm : 9 meters, the new length of the garden is 63 meters and the new width of the garden is 15.75 meters.
• The new length of the garden is 3 times as long as the original length of the garden.