the perimetre of rectangle is 240cm .if length is increased by 10% and breadth is decreased by 20% the perimetre remains same. find the length
Please explain clearly
To solve this problem, we need to set up an equation based on the given information and then solve for the length of the rectangle.
Let's start by assuming the length of the rectangle is "L" and the breadth is "B".
We are given that the perimeter of the rectangle is 240 cm, which can be calculated using the formula:
Perimeter = 2 * (Length + Breadth)
From the given information, we know that if the length is increased by 10% and the breadth is decreased by 20%, the perimeter remains the same.
So, we can write the equation as:
2 * (L + B) = 2 * (1.10L + 0.80B)
Simplifying the equation, we get:
L + B = 1.10L + 0.8B
Now, let's solve the equation to find the value of L.
Subtract 0.8B from both sides:
L + B - 0.8B = 1.10L
0.2B = 0.10L
Divide both sides by 0.10:
2B = L
From the equation, we can determine that the length of the rectangle is twice the breadth.
Since the perimeter remains the same after the changes, we can set up another equation using the new length and breadth:
2 * (1.10L) + 2 * (0.80B) = 240
Simplifying the equation:
2.20L + 1.60B = 240
Since we know that 2B = L, we can substitute it into the equation:
2.20(2B) + 1.60B = 240
4.40B + 1.60B = 240
6B = 240
Divide both sides by 6:
B = 40
Substitute the value of B back into 2B = L:
2(40) = L
L = 80
Therefore, the length of the rectangle is 80 cm.
2l + 2w = 240
l + w = 120
l = 120-w
new length = 1.1l
new width = .8w
2(1.1l) + 2(.8w) = 240
1.1l + .8w= 120
1.1(120-w) + .8w = 120
11(120-w) + 8w = 1200
1320 - 11w + 8w = 1200
-3w = -120
w = 40
then l = 120-40 =80
state a proper conclusion
can't understand what it is said
2(x+y) = 240
2(1.1x+0.8y) = 240
now solve for x.