The Parthenon has a rectangular base with a perimeter of 202 m and the area of the base is 2170 m^2.
Let L denote the length of the base and W denote the the width of the base.
As the perimeter is 202, 2*W + 2*L = 202
=> W + L = 101
=> W = 101 - L ...(1)
As the area is 2170, W*L = 2170
Substitute W from (1)
=> (101 - L)*L = 2170
=> 101*L - L^2 = 2170
=> L^2 - 101*L + 2170 = 0
=> L^2 - 31L - 70L + 2170 = 0
=> L(L - 31) - 70(L - 31) = 0
=> (L - 70)(L - 31) = 0
=> L = 31 and L = 70
The dimensions of the base are: length = 70 m and width = 31 m.
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