The difference between the length and the breadth of the rectangular paper, having a perimeter of 100 cm, and an area of 600 square cm, is <u>10 cm</u>.
In the question, we are given that the perimeter of rectangular paper is 100 cm and the area is 600 square cm.
We are asked to find the difference of length and breadth of the paper.
We assume the length and the breadth of the paper to be l cm and b cm respectively.
By the formula of the perimeter, the perimeter of the rectangular paper is 2(l + b) cm.
But, the value for the perimeter of the paper is given to be 100 cm.
Thus, we get an equation, 2(l + b) = 100, or, l + b = 50.
Also, its area = lb square cm.
The value for the area is given to be 600 square cm.
Thus, the equation we get is, lb = 600.
We are asked to find the difference between the length and the breadth of the paper, that is, l - b, assuming l >b.
Now, we know that, (x - y)² = (x + y)² - 4xy.
Putting l as x, and b as y, we get:
(l - b)² = (l + b)² - 4lb.
Substituting the values of l + b = 50, and lb = 600, we get:
(l - b)² = (50)² - 4(600),
or, (l - b)² = 2500 - 2400,
or, (l - b)² = 100,
or, l - b = √100,
or, l - b = 10.
Thus, the difference between the length and the breadth of the rectangular paper, having a perimeter of 100 cm, and an area of 600 square cm, is <u>10 cm</u>.
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