The algebraic expression that represent its area is x² - 12x + 35
The measurements of the land so that the area is 1,760 m² is 42.964m by 40.964m
The perimeter of the land is 167.856 m
The sides of the rectangle are (x - 5) and (x - 7) .
The area of a rectangle is represented as follows:
area = lw
where
l = length
w = width
Therefore, the algebraic representation of the area can be represented as follows;
area = (x - 5)(x - 7) = x² - 7x - 5x + 35 = x² - 12x + 35
The measurement of the land so that the area will be 1760 m² can be calculated as follows:
x² - 12x + 35 = 1760
x² - 12x - 1725 = 0
using the quadratic formula,
-b ±√b²- 4ac / 2a
a = 1
b = - 12
c = - 1725
Therefore,
x = 12 + 2√1761 / 2
x = 47.964
or
x = 12 - 2√1761 / 2
or - 35.964
x can't be negative because it does not fit in for the sides of the rectangle. so we have to use x = 47.964.
The measurements will be as follows:
(47.964 - 5)(47.964 - 7).
The measurement will be approximately 42.964m by 40.964m.
The perimeter will be as follows:
perimeter = 2(42.964 + 40.964) = 167.856 m.
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