The perimeter of a rectangular plot is 180m and its area is 1800m². Take the lenght of the plot as 'x'm . Use the perimeter 180m to write the value of the breadth in terms of 'x' . Use the value of lenght , breadth , and the area to write an equation in 'x' . Solve the equation to calculate the lenght and breadth of the plot.
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Answers
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solution
let the length be x
and breadth be y.
Perimeter of rectangle = 2(l+b)
It is given that perimeter is 180 m.
So, 2(x+y) = 180
x + y = 90
y = 90 - x ..........(i)
Area of rectangle = lb
It is given that the area is 1800 m².
So, xy= 1800 .............(ii)
Putting value of y from (i) in (ii),
x(90-x) = 1800
90x - x² - 1800 = 0
Dividing whole equation by (-),
-90x +x² +1800 = 0
x² - 90x + 1800 = 0
x² - 60x - 30x + 1800 = 0
x (x-60) - 30(x-60) = 0
(x-30) (x-60)=0
x = 30 and x=60.
Hence, x = 30 m and 60 m.
Therefore, there are two possible lengths 30m and 60m.
and y = 90-x
= 90 - 30 = 60m
and 90 - 60 = 30m.
Hence, two possible pair are length = 30m and breadth = 60m.
But, this is not possible as length is never greater to breadth.
So, the possible length is 60 m and breadth is 30 m.
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