To find the length of the diagonal fence that divides a rectangular garden measuring 30 feet by 24 feet, we can use the Pythagorean theorem. The diagonal acts as the hypotenuse of a right triangle formed by the length and width of the rectangle.
The formula for the Pythagorean theorem is:
\[ c = \sqrt{a^2 + b^2} \]
where:
- \( c \) is the length of the diagonal,
- \( a \) is the length of one side (30 feet),
- \( b \) is the length of the other side (24 feet).
Plugging in the values:
\[ c = \sqrt{30^2 + 24^2} \] \[ c = \sqrt{900 + 576} \] \[ c = \sqrt{1476} \] \[ c \approx 38.4 \text{ feet} \]
Thus, the length of the fence should be approximately 38.4 feet.
5 answers