Four squares gardens have the following in square meters: 144,32,72,and 250. Which area had a rational numbers as the side length?
A rational number is a number that can be expressed as a fraction of two integers. The square of a rational number will also be a rational number.
The area of a square is equal to the side length squared. Therefore, if the area is a rational number, the side length must also be a rational number.
Out of the given areas, 144, 32, 72, and 250, the only one that has a rational side length is 144.
The side length of the square with an area of 144 square meters is √144 = 12, which is a rational number because it can be expressed as 12/1.
To determine which area had a rational number as the side length, we need to check if the area of a square has a rational square root.
First, we calculate the square root of each area:
- Square root of 144: √144 = 12
- Square root of 32: √32 ≈ 5.66
- Square root of 72: √72 ≈ 8.49
- Square root of 250: √250 ≈ 15.81
From the calculations, we can see that the only area that has a rational square root is 144. Therefore, the square with an area of 144 square meters had a side length that was a rational number.