Answer:
8 , 40
Explanation:
The area of a rectangle is calculated by multiplying the length by the width. In this case, the area is given as 320 ft².
So, we can set up the following equation:
x * (10x - 40) = 320
Simplifying the equation:
10x^2 - 40x - 320 = 0
Dividing the equation by 10 to simplify further:
x^2 - 4x - 32 = 0
To solve this quadratic equation, we can factorize or use the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -4, and c = -32. Plugging these values into the formula:
x = (-(-4) ± √((-4)^2 - 4(1)(-32))) / (2(1))
x = (4 ± √(16 + 128)) / 2
x = (4 ± √144) / 2
x = (4 ± 12) / 2
x = (4 + 12) / 2 or x = (4 - 12) / 2
x = 16 / 2 or x = -8 / 2
x = 8 or x = -4
Since the dimensions of a rectangle cannot be negative, we discard the solution x = -4.
Therefore, the length of one side is 8 ft.
The other side can be found by substituting this value back into the expression "10x - 40":
10 * 8 - 40 = 80 - 40 = 40 ft
Therefore, the lengths of the sides of the rectangle are 8 ft and 40 ft, respectively.