Question

Foursquare gardens have the following areas in square meters: 144, 32, 72, and 250. Which area has a rational number of meters as the side length

Answer 1

To find which areas have a rational number of meters as the side length, we need to find the square root of each area and check if it is a rational number. A number is rational if it can be expressed as the quotient of two integers.

1. For an area of **144 m²**:
\[
\sqrt{144} = 12 \quad (\text{rational})
\]

2. For an area of **32 m²**:
\[
\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2} \quad (\text{irrational})
\]

3. For an area of **72 m²**:
\[
\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \cdot \sqrt{2} = 6\sqrt{2} \quad (\text{irrational})
\]

4. For an area of **250 m²**:
\[
\sqrt{250} = \sqrt{25 \times 10} = \sqrt{25} \cdot \sqrt{10} = 5\sqrt{10} \quad (\text{irrational})
\]

The only area that has a rational number as the side length is **144 m²**, which has a side length of **12 meters**.