SOLUTION: Fans can now have a better view of wolverine football, after the instillasion of 40% larger screens in Michigan stadium's end zones. Each screen covers 3995ft^2 of a new 6696 squar

Click here to see ALL problems on Quadratic Equations

Question 972058: Fans can now have a better view of wolverine football, after the instillasion of 40% larger screens in Michigan stadium's end zones. Each screen covers 3995ft^2 of a new 6696 square foot scoreboard structure.
A) the screen in Michigan Stadium is a rectangle with length 9ft less than twice its width. Find the length and width of the screen.
B) the scoreboard structure is a rectangle with length 16ft less than twice its width. Find the length and width of the scoreboard.
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
width= x length is 2x-9
Product is x(2x-9) = 3995 ft^2 ft *ft on the left, so units are fine.
2x^2-9x-3995=0 factors are 799 and 5
look at discriminant b^2-4ac=32041, and perfect square of 179 (81+ 4*2*3995)
x=-(1/4) {9+/- 179)
negative answer not used. (1/4) 188=47 That is width. Length is 85. product is 3995 ft^2
Scoreboard structure
x=width
2x-16=length
x(2x-16)=6696
2x^2-16x-6696=0
x^2-8x-3348=0 (divide by two)
again, look at discriminant sqrt(b^2-4ac) =sqrt{ 64+ (4*3348)}=116
x= (1/2) [8+116] (negative root extraneous) =124
width is 62
length is 108
product is 6696 ft^2