To find the distance from stake Z to stake X, we can use the Pythagorean theorem. The distance from stake X to stake Y is 24 yards, and the distance from stake Y to stake Z is 18 yards. Since the strings meet at a right angle, the distances form a right triangle.
The sides of this triangle are:
- One side (XY) = 24 yards
- The other side (YZ) = 18 yards
- The hypotenuse (ZX) is what we need to find.
According to the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the hypotenuse (ZX), and \( a \) and \( b \) are the other two sides (XY and YZ).
Substituting in our values:
\[ ZX^2 = XY^2 + YZ^2 \] \[ ZX^2 = 24^2 + 18^2 \] \[ ZX^2 = 576 + 324 \] \[ ZX^2 = 900 \]
Now, take the square root to find ZX:
\[ ZX = \sqrt{900} = 30 \text{ yards} \]
So, the distance from stake Z to stake X is 30 yards.
The correct answer is A. 30 yards.
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