1. The length of a rectangle is 6 inches longer than thrice its width. The area of the rectangle is 57 square inches. Write a quadratic equation for the area of the floor in terms of x. Find the length and width of the rectangle.

Question

1.  The length of a rectangle is 6 inches longer than thrice its width. The area of the rectangle is 57 square inches. Write a quadratic equation for the area of the floor in terms of x. Find the length and width of the rectangle.
2.  If 1,500 ft of fencing is available to build and fence ten adjacent pens, express the total area of the pens in terms of x. What value of x and y will maximize the total area? Find the total area of the field.

Reiny · Answer

width --- x
length -- 3x + 6

x(3x+6) = 57
3x^2 + 6x - 57 = 0
x^2 + 2x - 19 = 0
I am going to complete the square, easier in this case than the formula
x^2 + 2x + 1 = 19+1
(x+1)^2 = 20
x+1 = ± √20
x = -1 ± √20
= appr 3.472 or a negative

width = 3.472 , lenght is 16.416

Perhaps you were supposed to use 2 variables
then width = x
length = y

but y = 3x+6 , and area = xy = x(3x+6)
and we are back to the way I did it at the top

2.
Your "English" of the first sentence makes no sense to me. How is x defined? Where does y come in?
Tell me what your definitions are.