The area of a rectangle is 54cm. the length is 2cm more than a x and the width is 5cm less than twice x. solve for x. round your answer to the nearest whole number.

A rectangle is a quadrilateral and its area is expressed as the product of its length and width. From the given, we have:

Length = x + 2
Width = 2x - 5
Area = 54 cm^2

Area = Length x Width
Substituting the values,
Area = (x + 2) ( 2x-5) = 54
54 = 2x^2 - x - 10
2x^2 - x - 64 = 0

We can see that the equation above is a polynomial with a degree of 2 therefore we can usethe Quadratic Formula to solve for x. The quadratic formula will solve two values of x.

x1 = (-b + (√b^2 - (4ac))/ 2a = 5.91
x2 = (-b - (√b^2 - (4ac))/ 2a = -5.41

Since, for this case, the value x should not result to a negative value  for both dimensions thus x is equal to 5.91.