Respuesta :
Answer:
width = 36
length = 109
Step-by-step explanation:
width: x
length: 4x - 35
x * (4x - 35) = 3924
4x^2 - 35x = 3924
4x^2 - 35x - 3924 = 0
(4x + 109)(x - 36) = 0
x = -109/4 or x = 36
Obviously we have to use x = 36 because you can't have a rectangle with negative lengths and widths lol.
width = 36
length = 4(36) - 35 = 144 - 35 = 109
Answer:
Step-by-step explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
A rectangle has a length of 35 feet less than 4 times its width. This means that
L = 4W - 35
The area of a rectangle is expressed as L×W = LW
If the area of the rectangle is 3924 square feet, it means that
LW = 3924 - - - - - - -1
Substituting L = 4W - 35 into equation 1, it becomes
W(4W - 35) = 3924
4W^2 - 35W = 3924
4W^2 - 35W - 3924 = 0
4W^2 + 109W - 144W - 3924 = 0
W(4W + 109) -36(4W + 109) = 0
(W - 36)(4W + 109) = 0
W - 36 = 0 or 4W + 109 = 0
W = 36 W = -109/4 = - 27.25
Since the width cannot be negative, the width will be 36 feet
The length will be 3924/36 = 109 feet
