Question

There are two fields at the park. Field 1 is rectangular, with dimensions of 60 yards by 30 yards. Field 2 has dimensions that are double those of Field 1.
Which statement accurately describes the area of Field 1 in relation to the area of Field 2?
The area of field 1 is 116 the area of field 2.
The area of field 1 is 18 the area of field 2.
The area of field 1 is 14 the area of field 2.
The area of field 1 is 12 the area of field 2.

Answer 1

To determine the area of each field and compare them, we start by calculating the area of Field 1.

Field 1 is rectangular with dimensions:
- Length = 60 yards
- Width = 30 yards

The area of Field 1 (A1) is calculated as:
\[
A1 = \text{Length} \times \text{Width} = 60 \, \text{yards} \times 30 \, \text{yards} = 1800 \, \text{square yards}
\]

Next, we consider Field 2, which has dimensions that are double those of Field 1:
- Length = 2 × 60 yards = 120 yards
- Width = 2 × 30 yards = 60 yards

The area of Field 2 (A2) is calculated as:
\[
A2 = \text{Length} \times \text{Width} = 120 \, \text{yards} \times 60 \, \text{yards} = 7200 \, \text{square yards}
\]

Now, we compare the areas of Field 1 and Field 2:

To find the ratio of the area of Field 1 to the area of Field 2:
\[
\frac{A1}{A2} = \frac{1800 \, \text{square yards}}{7200 \, \text{square yards}} = \frac{1}{4}
\]

This can also be stated as:
- The area of Field 1 is \(\frac{1}{4}\) the area of Field 2.

Now, we can analyze the statements given:

- "The area of Field 1 is 1/16 the area of Field 2." - **False**
- "The area of Field 1 is 1/8 the area of Field 2." - **False**
- "The area of Field 1 is 1/4 the area of Field 2." - **Correct**
- "The area of Field 1 is 1/2 the area of Field 2." - **False**

Therefore, the statement that accurately describes the area of Field 1 in relation to the area of Field 2 is:
**The area of Field 1 is 1/4 the area of Field 2.**