Question

The area of rectangular land of Suhas's is 500 sq. meter. If length of land is decreased by 3 metre and breadth is increased by 2 meter, then the land formed a square. Let us write by calculating the length and breadth of land of Suhas's.

Heeellpp and No spams ​

Answer 1

$\huge\bf\underline\blue{Answer}$

The length of the land is 25 m and the breadth of the land is 20 m respectively.

Explanation:-

$\bf\underline\red{Given :}$

$\bullet$ Area of rectanglular land = 500 m²

$\bullet$ When the length is decreased by 3 metre and the breadth is increased by 2 metre, the land forms a square.

$\bf\underline\purple{To \: find :}$

The length and breadth of the land

$\bf\underline\green{Solution :}$

Let the length be 'l' m

and the breadth be 'b' m

We know that,

=> Length × Breadth = Area

=> l × b = 500

Now,

New length = (l - 3) m

and new breadth = (b + 2) m

As it forms a square, The sides of square are the same. So :-

=> l - 3 = b + 2

=> l = b + 2 + 3

=> l = b + 5

Now,

Putting the value of l :-

=> l × b = 500

=> (b + 5) × b = 500

=> b² + 5b = 500

=> b² + 5b - 500 = 0

=> b² + (25 - 20)b - 500 = 0

=> b² + 25b - 20b - 500 = 0

=> b(b + 25) - 20(b + 25) = 0

=> (b - 20) (b + 25) = 0

Either, (b + 25) = 0 or, (b - 20) = 0

•b + 25 = 0

=> b = -25 (Neglected)

•b - 20 = 0

=> b = 20

Hence, the breadth of the rectangular field is 20 m.

Therefore:-

$= > length = \dfrac{area}{b} \: m$

$= > length = \dfrac{500}{20} \: m$

$= > length = 25 \: m$

Hence, the length of length of the field is 25 m.

Answer 2

Answer:

________________________________

Consider the length be 'l' m

and the breadth be 'b' m

Length = Area

→ l × b = 500

________________________________

New length = (l - 3) m

New breadth = (b + 2) m

As it forms a square, The sides of square are the same. So :-

= l - 3 = b + 2

= l = b + 2 + 3

= l = b + 5

________________________________

★ Put the value of l :-

= l × b = 500

= (b + 5) × b = 500

= b² + 5b = 500

= b² + 5b - 500 = 0

= b² + (25 - 20)b - 500 = 0

= b² + 25b - 20b - 500 = 0

= b(b + 25) - 20(b + 25) = 0

= (b - 20) (b + 25) = 0

It can be (b + 25) = 0 or, (b - 20) = 0

• b + 25 = 0

= b = -25 (It is Neglected)

•b - 20 = 0

= b = 20

The breadth of the rectangular field is 20 m.

________________________________

★ Hence ;

= Length = $\tt{\dfrac{Area}{b} \: m}$

= Length = $\tt{\dfrac{500}{20} \: m}$

= length = 25 m

The length of length of the field is 25 m.