the area of rectangular land of suhas's is 500 m2. if the length of the land decreased by 3 meter 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.
Answers
Step-by-step explanation:
The length of the land is 25 m and the breadth of the land is 20 m respectively.
Explanation:-
\bf\underline\red{Given :}
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 :}
Tofind:
The length and breadth of the land
\bf\underline\green{Solution :}
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=
b
area
m
= > length = \dfrac{500}{20} \: m=>length=
20
500
m
= > length = 25 \: m=>length=25m
Hence, the length of length of the field is 25 m.