The perimeter of a rectangle is 240m. If its length is decreased by 10% and breadth is increased by 20% we get the same perimeter. Find the length and the breadth of the both the rectangles.
Answers
the answer is solved above
please mark me brainlist
Given :-
The perimeter of a rectangle is 240m. If its length is decreased by 10% and breadth is increased by 20% we get the same perimeter
To Find :-
Length and breadth
Solution :-
Let the length be l and breadth be b
P = 2(l + b)
240 = 2(l + b)
240/2 = l + b
120 = l + b (1)
When Length decreased by 10%
l - 10% of l
l - 10/100 × l
l - 10l/100
100l - 10l/100
90l/100
9l/10
Breadth increased by 20%
b + 20/100 × b
b + 20b/100
100b + 20b/100
120b/100
12b/10
Now,
2(9l/10 + 12b/10) = 240
9l/10 + 12b/10 = 240/2
9l + 12b/10 = 120
9l + 12b = 120(10)
9l + 12b = 1200
Divide by 3
9l + 12b/3 = 1200/3
3l + 4b = 400 (2)
Now,
Multiply 1 by 3
3(l + b) = 3(120)
3l + 3b = 360
On solving
3l + 4b - 3l - 3b = 400 - 360
4b - 3b = 40
b = 40
Now,
3l + 4b = 400
3l + 4(40) = 400
3l + 160 = 400
3l = 400 - 160
3l = 240
l = 240/3
l = 80
Therefore
Length is 80 cm and breadth is 40 cm