A rectangular Corn Hole area at the recreation center has a width of 5 feet and a length of 10 feet. If a uniform amount is added to each side, the area is increased to 84 square feet. What is the amount added to each side?
Let x be the amount added to each side.
The original area of the Corn Hole area is width * length = 5 * 10 = 50 square feet.
After adding x to each side, the new width is 5 + 2x and the new length is 10 + 2x.
The new area is (5 + 2x)(10 + 2x) = 84.
Expanding this equation, we get:
50 + 20x + 4x^2 = 84
Rearranging the equation:
4x^2 + 20x - 34 = 0
Dividing by 2, we get:
2x^2 + 10x - 17 = 0
We can solve this quadratic equation using the quadratic formula:
x = (-10 ± √(10^2 - 4*2*(-17))) / 2*2
x = (-10 ± √(100 + 136)) / 4
x = (-10 ± √236) / 4
x = (-10 ± √236) / 4
x = (-10 ± 15.36) / 4
Thus, x is about 1.84 feet.
Therefore, the amount added to each side is approximately 1.84 feet.