# The Parthenon is a temple with a rectangular base. The perimeter of the base is 202 m and the area is 2170 m^2. Find the dimensions of the base.

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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.**

Let L be the length of the base and W be the the width of the base.

area of the base(rectangle) =L*W=2170

The perimeter of the base(rectangle)=2(L+W)=202

L+W=202/2

L+W=101 -----(1)

(L-W)^2= (L+W)^2 -4LW

= 101^2 - 4*2170

= 10201 - 8680

=1521

L-W =39------------(2)

L+W=101 -----(1)

L-W =39------------(2)

Adding 2L =140

L=70

Substiututing L value in equation 1 we get

70+W=101

W=101 - 70

W=31

**The dimensions of the base are: length = 70 m and width = 31 m.**