To find the height of the square-based pyramid, we can use the formulas for the area of the base and the volume of a pyramid.
-
The area of the base (which is a square) is given by: \[ A = s^2 \] where \( s \) is the length of one side of the square base. Since the area is given as 50 square yards, we have: \[ s^2 = 50 \quad \Rightarrow \quad s = \sqrt{50} = 5\sqrt{2} \text{ yards} \]
-
The volume \( V \) of the pyramid is given by: \[ V = \frac{1}{3} A_{base} \times h \] where \( A_{base} \) is the area of the base, and \( h \) is the height of the pyramid. We know the volume is 250 cubic yards, so we can set up the equation: \[ 250 = \frac{1}{3} \times 50 \times h \]
-
Simplifying this equation: \[ 250 = \frac{50h}{3} \] \[ 250 \times 3 = 50h \] \[ 750 = 50h \] \[ h = \frac{750}{50} = 15 \text{ yards} \]
Thus, the height of the pyramid is \( \boxed{15} \) yards.