Four square 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?(1 point)

Answer 1

To determine which area has a rational number of meters as the side length, we need to take the square root of each area, since the side length of a square garden is the square root of its area. A square root is rational if the area is a perfect square.

1. Area = 144
   \(\sqrt{144} = 12\) (rational)

2. Area = 32
   \(\sqrt{32} = \sqrt{16 \cdot 2} = 4\sqrt{2}\) (irrational)

3. Area = 72
   \(\sqrt{72} = \sqrt{36 \cdot 2} = 6\sqrt{2}\) (irrational)

4. Area = 250
   \(\sqrt{250} = \sqrt{25 \cdot 10} = 5\sqrt{10}\) (irrational)

Thus, the only area with a rational number of meters as the side length is 144 square meters.