The area of a rectangular land is 500 sq.m.If the length is decreased by 3m and breadth is increased by 2m.then land formed a square.let us write by calculating the length and breadth of land?

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Answer 1 · 2017-08-23T09:02:41

see explanation

Let #l and b# be the length and breadth of the rectangular land, respectively.

Area of the rectangular land #=l*b=500#

#=> b=500/l# -------{1}

We know that a square has four equal sides.
Given that if the length is decreased by 3m and breadth is increased by 2m, then the land forms a square,

#=> (b+2)=(l-3)#

#b=l-5#

Substituting #(b=l-5)# into {1} gives

#l-5=500/l#

#=> l^2-5l-500=0#

#=> (l-25)(l+20)=0#

#=> l=25 or -20#

As #l# can not be negative, #=> l=25#

#=> b=l-5=25-5=20#

Hence, length of rectangle #l=25 " m"#
and breadth of rectangle #b= 20 " m"#.

I hope that helps!