if one side of a square is increased by 2metres and other side is reduced by 2 metres. a rectangle is formed whose perimeter is 48.find the side of the orignal square.
If you reduce one side by the same amount of what you increase on another side, the differences should cancel out. Thus the perimeter should stay the same, easily leaving 48(Perimeter of your rectangle AND square) to be divided by 4 (sides of a square).
proof of what Justin said:
let sides of original square be x by x
perimeter = 4x
new length = x+3
new width = x-3
new perimeter = 2(x+3) + 2(x-3)
= 2x + 6 + 2x - 6
= 4x , just as before
so original side = 84/4 = 21
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To find the side of the original square, we can use the information given in the problem.
Let's assume that the side of the original square is "x" meters.
According to the problem, if one side of the square is increased by 2 meters and the other side is reduced by 2 meters, a rectangle is formed.
So, the dimensions of the rectangle would be (x + 2) and (x - 2).
We are also given that the perimeter of the rectangle is 48 meters.
Perimeter of a rectangle is given by the formula: Perimeter = 2 * (length + width)
Substituting the given values, we can write the equation as:
48 = 2 * ((x + 2) + (x - 2))
Simplifying the equation, we have:
48 = 2 * (2x)
Dividing both sides by 2, we get:
24 = 2x
Dividing both sides by 2 again, we get:
12 = x
Therefore, the side of the original square is 12 meters.