A gardener wants to divide a square piece of lawn in half diagonally. what is the length of the diagonal side of the square is 8 fr. leave your answer in simplest radical form.
To divide a square piece of lawn in half diagonally, we can draw a line from one corner of the square to the opposite corner. This line represents the diagonal side of the square.
Since we are given that the length of the diagonal side of the square is 8 ft, we know that the length of this line is 8 ft.
By applying the Pythagorean theorem, we can find the length of one of the sides of the square.
Let's assume that the length of one of the sides of the square is x ft. According to the Pythagorean theorem:
\[x^2 + x^2 = 8^2\]
\[2x^2 = 64\]
\[x^2 = 32\]
Now, let's simplify x^2 = 32 by taking the square root of both sides:
\[x = \sqrt{32}\]
\[x = \sqrt{16 \cdot 2}\]
Since \(\sqrt{16} = 4\), we can simplify further:
\[x = 4 \sqrt{2}\]
Therefore, the length of one side of the square is \(4 \sqrt{2}\) ft.