Perimeter of rectangle is 240cm if it's length is decreased by 10 percent and breadth is increased by 20 percent we get the same perimeter find the length and breadth of the rectangle
x+y=120
0.9x + 1.2y = 120
80+40 = 120
72+48 = 120
width --- w
length --- l
2l + 2w = 240
l + w = 120 ---- l = 120-w **
new width = 1.2w
new length = .9l
2(1.2w) + 2(.9l) = 240
2.4w + 1.8l = 240
24w + 18l = 2400
divide by 6
4w + 3l = 400
sub in **
4w + 3(120-w) = 400
4w + 360 - 3w = 400
w = 40
then in ** , l = 80
the original rectangle was 40 cm by 80 cm
check: Perimeter = 2(40) + 2(80) = 240
changed rectangle was 48 by 72
perimeter of changed rectangle
= 2(48) + 2(72) = 240
To find the length and breadth of the rectangle, we can start by setting up equations based on the given information.
Let's assume the original length of the rectangle is L and the original breadth is B.
According to the given information, the perimeter of the rectangle is 240 cm. The formula for the perimeter of a rectangle is P = 2L + 2B, where P is the perimeter, L is the length, and B is the breadth.
So, we have the equation:
2L + 2B = 240 ----(1)
Now, we are given that the length is decreased by 10 percent and the breadth is increased by 20 percent, resulting in the same perimeter.
When the length is decreased by 10 percent, it becomes:
L decreased by 10 percent = L - (0.1 * L) = 0.9L
When the breadth is increased by 20 percent, it becomes:
B increased by 20 percent = B + (0.2 * B) = 1.2B
Now, using the new length (0.9L) and breadth (1.2B), we can set up the new equation for the perimeter:
2(0.9L) + 2(1.2B) = 240
Simplifying this equation, we get:
1.8L + 2.4B = 240 ----(2)
Now, we have a system of equations with equations (1) and (2). We can solve these equations simultaneously to find the values of L and B.
Let's solve these equations to find the length (L) and breadth (B) of the rectangle.
Equation (1): 2L + 2B = 240
Equation (2): 1.8L + 2.4B = 240
Multiplying equation (1) by 1.2 to make the coefficients of B the same as in equation (2), we get:
1.2 * (2L + 2B) = 1.2 * 240
2.4L + 2.4B = 288 ----(3)
Now, we can subtract equation (3) from equation (2):
(1.8L + 2.4B) - (2.4L + 2.4B) = 240 - 288
-0.6L = -48
Dividing both sides by -0.6:
L = -48 / -0.6
L = 80
Now, we can substitute the value of L back into equation (1) to find B:
2L + 2B = 240
2(80) + 2B = 240
160 + 2B = 240
2B = 240 - 160
2B = 80
Dividing both sides by 2:
B = 80 / 2
B = 40
Therefore, the length of the rectangle is 80 cm and the breadth of the rectangle is 40 cm.