the area of a rectangle is 77m to the second power and the length of the rectangle is 3m more then twice the width. find the dimensions

The length is 14 m, and the width is 5.5 m.

Step-by-step explanation:

Let the width = x

The length is 2x + 3

area = length * width

77 = (2x + 3)x

2x^2 + 3x = 77

2x^2 + 3x - 77 = 0

(2x - 11)(x + 7) = 0

2x - 11 = 0  or  x + 7 = 0

2x = 11 or x = -7

x = 5.5 or x = -7

Since the width of a rectangle cannot be a negative number, we discard the solution x = -7.

x = 5.5

The length is 2x + 2 = 2(5.5) + 3 = 11 + 3 = 14

The length is 14 m, and the width is 5.5 m.