Problema Solution
Sean has a large vegetable garden that is in the shape of a right angle. The sides of the right triangle measure 10 ft, 24 ft, and 26 ft. He wants to place a sprinkler so that it will water the entire garden, but he wants to keep the wasted water to a minimum. Where should he place the sprinkler? What percentage of the water will fall outside of the garden?
Answer provided by our tutors
We will assume the sprinkler sprinkles water in an area of a circle with radius r.
To keep the wasted water to a minimum he must put the sprinkle at the middle point of the hypotenuse of the right triangle. That is why the radius of the area will be r = 26/2 = 13 ft.
The area of the sprinkled surface is:
A1 = r^2*pi
A1 = 13^2*pi
A1 = 169pi ft^2
The area of the garden is:
A = (1/2)10*24
A = 120 ft^2
The percentage of the water that will fall outside the garden is:
(A1 - A)/A1 = (169*pi - 120)/169pi = (169*3.14 - 120)/(169*3.14) = 0.774 or 77.4%