Answer: Length = 70 meters
Width = 31 meters
Step-by-step explanation:
Let the width of the rectangle be x.
Since the length of the base of the Parthenon is 8 meters more than twice its width. This will be: = 2x + 8
Area = 2170
Since length × width = area
(2x + 8) × x = 2170
2x² + 8x = 2170
Divide through by 2
x² + 4x = 1085
x² + 4x - 1085 = 0
x² + 35x - 31x - 1085 = 0
x(x + 35) - 31(x + 35) = 0
(x + 35) = 0 or (x - 31) = 0
x - 31 = 0
x = 0 + 31
x = 31
Width = 31 meters
Length = 2x + 8
= 2(31) + 8
= 62 + 8
= 70 meters
The rectangular base has a length of 70 meters and a width of 31 meters.
Area is the amount of space occupied by a two dimensional object or figure. The area (A) of a rectangle is:
A = length * width
Let w represent the width, hence:
l = 2w + 8
Area = (2w + 8)w
2170 = 2w² + 8w
2w² + 8w - 2170 = 0
w = 31 m
l = 2(31) + 8 = 70 m
The rectangular base has a length of 70 meters and a width of 31 meters.
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