
Tim T. answered 05/07/20
Math: K-12th grade to Advanced Calc, Ring Theory, Cryptography
Greetings! Lets solve this shall we ?
So, we must find the dimensions of this rectangular flower bed given the area of 11.76 square feet and the width of 3.5 feet less than the length. This translates into w = x - 3.5, where the length is l = x. Then, we yield the area of a rectangle such that
l*w = A
(x)(x-3.5) = 11.76.........Distribute the x inside to obtain
x2 - 3.5x = 11.76.......Then subtract 11.76 to the other side to obtain
x2 - 3.5x - 11.76 = 0........Then we try and factor and notice we must use the Quadratic Formula such that
a = 1 , b = -3.5 and c = -11.76. Then
3.5 ± √(12.25 + 47.04) / 2 = 3.5 ± √(59.29) / 2 = (3.5 + 7.7) / 2 = x = 5.6....We only use the positive x value because the other one is negative and we cannot have a negative length. So, the length is x = 5.6 feet.
Now we can find the width such that w = 5.6 - 3.5 = 2.1 feet.
I hope this helped!