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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