Question

the perimeter of a rectangle is 120m. If the length is decreased by 5m and the breadth is increased by 10m, then, area increased by 250m^2. Find the length and breadth of the rectangle

Answer 1

This is very easy first we have to subtract 120-5=115+10=125/10=12.5 is the length and the breadth is 12.5/125=0.1 so the breadth is 0.1 and the length is 12.5

Answer 2

Perimeter of a rectangle with sides l and b is 2(l+b),

According to the question , If we assume Length is l and breadth is b, Then
2(l+b) = 120 m,
=> l +b = 60 m,
=> l = 60 - b m, ------------(1),

And Area of a rectangle with sides l and b is l*b,
Now, For this rectangle the area is (60-b)(b) , It is Initial Area,
=> Initial Area = (60-b)(b),
=> Initial Area = 60b -b²

According to the question , 
If  Breadth is increased by 10 m, And If length is decreased by 5 m, Then the area is increased by 250 m²,

=> New area = 250 m² + Initial Area,

New area is (l-5)*(b+10),
We already saw that from (1) l = 60 -b ,
=> New area = (60-b-5)*(b+10),
=> New area = (55-b)(b + 10),
=> New area = 55b + 550 -b² - 10b
=> New area = -b² + 45b + 550,

Now,
-b² + 45b + 550 = (60b - b²) + 250 m²,
=> 45b + 550 = 60b + 250,
=> 300 = 15b,
=> b = 20 m,

Now length = 60 - 20 = 40 m,

Therefore the Length of Rectangle is 40 m, Where as The breadth is 20 m ,

Hope you understand,Have a Great day !,
Thanking you, Bunti 360 !