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!