a perimeter of a rectangle is 240 cm . If its length is decreased by 10% and its breath is increased by 20% . We get the same perimeter . Find the Length and breath
Answers
Answer:
Step-by-step explanation:
perimeter of rectangle = 2(l+b)
240 = 2(l+b)
l+b =120
l=120-b
now
length is decreased by 10% and its breath is increased by 20%
new length, L =0.9l ,new breadth B = 1.2b
permieter = 2(L+B)
240 = 2(0.9l+1.2b)
0.9l+1.2b=120
0.9(120-b) + 1.2b = 120
108 - 0.9 b +1.2b = 120
0.3 b = 12
b =40cm
l =80 cm
Answer:
Step-by-step explanation:
Hi, my friend.
Let the length of the rectangle be m.
Let the breadth of the rectangle be n.
Hence Perimeter of a rectangle:
P => 2(m + n) = 240 cm
=> m + n = 120 cm
Multiply 4 on both sides. (We'll need it in future)
=> 4m + 4n = 480 cm ----------(1)
Now given that,
Length is decreased by 10%
Let the new length be x.
x = m - (10% of m)
=> x = m - (m/10)
=> x = (10m/10) - (1m/10)
=> x = (9m/10) cm --------(2)
Breadth is increased by 20%
Let the new breadth be y.
y = n + (20% of n)
=> y = n + (n/5)
=> y = (5n/5) + (n/5)
=> y = (6n/5)
=> y = (12n/10) cm ----------(3)
The perimeter of n rectangle
=> P => 2(x + y) = 240 cm (Given)
=> x + y = 120 cm -------------(4)
Substitute equations (2) and (3) in equation (4)
=> (9m/10) + (12n/10) =120
=> (9m + 12n)/(10) = 120
=> 9m + 12n = 1200
=> 3(3m + 4n) = 1200
=> 3m + 4n = 400 ---------(5)
Subtract equation (5) from equation (1)
i.e. equation (1) - equation (5)
Hence we get m = 80 cm
Substitute m value in equation (1)
We get n = 40 cm
Hence the length and breadth of the original rectangle is 80 cm, 40 cm.
Harith
Maths Aryabhatta
