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
Answer:
Step-by-step explanation:
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,
- The length and the breadth of the both the rectangles.
Solution:-
Let the length and breadth of the rectangle be x m and y m.
According to the Question,
⇒ x + y = 120 .... (i)
Length = x(100 - 10)/100
= 9x/10
Breadth = y(100 +20)/100
= 12y/10
Perimeter of rectangle = 240 m
2(L + B) = 240
⇒ 2(9x /10 + 12y /10) = 240
⇒ 9x + 12y = 1200
⇒ 3x + 4y = 400 .... (ii)
Solving Eq (i) and (ii), we get
⇒ y = 40
Putting y's value in Eq (i), we get
⇒ x + y = 120
⇒ x + 40 = 120
⇒ x = 120 - 40
⇒ x = 80
Length = x = 80 m
Breadth = y = 40 m
Hence, the length and the breadth of the rectangle are 40 m and 80 m.
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