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.