A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measure SL 42,000 ft2. What is the dimension of the parking lot?

Answer:[tex]L = 210[/tex],  [tex]W=200[/tex][tex]W=210[/tex],  [tex]L = 200[/tex]Step-by-step explanation:By definition, the perimeter of a rectangle is:[tex]P = 2L + 2W[/tex]Where:P is the perimeter, L is the length and W is the widthAlso, the area of a rectangle is:[tex]A = LW[/tex]Where L is the length of the base and W is the width.We know that for this rectangle:[tex]P = 2L + 2W = 820 ft\\\\A = LW = 42,000 ft ^ 2[/tex]Now we have two equations and two unknowns (L and W)Then we solve the system.[tex]L = \frac{42,000}{W}[/tex]Now we substitute this relation in the perimeter equation.[tex]2(\frac{42,000}{W}) + 2W = 820\\\\\frac{42,000}{W} + W = 410\\\\42000 + W ^ 2 = 410W\\\\W ^ 2 -410W + 42000 = 0\\\\(W - 210)(W - 200) = 0\\\\W = 210\\\\W = 200[/tex]Then for W=210:[tex]L = \frac{42000}{W}\\\\L = \frac{42000}{210}\\\\L = 200[/tex]And for W=200[tex]L = \frac{42000}{200}\\\\L = 210[/tex]