By definition, a rectangle is a quadrilateral (4-sided polygon) containing two sets of equal and parallel sides called the length and the width. For determining the area of a rectangle, you simply have to multiply length times width. In this problem, let L be the length and W be the width. Then, we formulate the two independent formulas: formula for area, and formula relating L and W
A = LW = 33
L = 2W-5
Substituting the second equation to the first,
A = 33 = (2W - 5)W
33 = 2W² - 5W
2W² - 5W -33 = 0
W = 5.5 and -3
Since the equation is quadratic, there are two possible roots: 5.5 and -3. However, we can only use the positive value. Thus, W=5.5 m. Consequently,
L = 2(5.5)-5
L = 6 m
Therefore, the dimensions of the rectangle is 6 m by 5.5 m.
