Question

perimeter of rectangle field is 2400 if the length is increased by 10%and breadth is decreased by20% we get the same perimeter find the length and breadth
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Answer 1

Step-by-step explanation:

Let the length of the rectangle field be l

Let the breadth of the rectangle field be b

We know that the perimeter of a rectangle = 2(l + b)

Therefore,

2(l + b) = 2400

l + b = 1200

The length is increased by 10%,

New length = l + (l * 10/100) = 11l/10

The breadth is decreased by 20%

New breadth = b - (b * 20/100) = 4b/5

New perimeter = 2(11l/10 + 4b/5) = 2[(11l + 8b)/10] = (11l + 8b)/5

According,

If we increase the length by 10% and the breadth is decreased by 20% then we get the original perimeter only

(11l + 8b)/5 = 2400

11l + 8b = 12000

Multiplying 8 on both sides on the equation l + b = 1200

8l + 8b = 9600

Subracting 8l + 8b = 9600 from 11l + 8b = 12000

11l + 8b - 8l - 8b = 12000 - 9600

3l = 2400

l = 800 m

Subtisute l = 800 m in the equation 8l + 8b = 9600

6400 + 8b = 9600

8b = 3200

b = 400 m

$\boxed{\rm The \: length \: is \: 800m \: and \: the \: breadth \: is \: 400m }$