Question

The perimeter of a rectangular plot is 180m and its area is 1800m2.cal l&b

Answer 1

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Answer 2

Hi


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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