A piece of length 1 meter is cut into two parts and each piece is bent to form a square.the Total area of the two squares forms is 325cm^2.Given that one of the pieces is X cm Long, find the area of the square formed from this piece in term of X.

Answer 1

Let the length of one of the pieces be X cm. So, the length of the other piece will be (100 - X) cm.

First, calculate the area of each square formed:
Let the side length of the square formed from the piece of length X cm be a cm,
Then, a = X/4 (since each side of the square formed is 1/4 of the original length)
Area of square formed from piece of length X = a^2 = (X/4)^2 = X^2/16 cm^2

Let the side length of the square formed from the other piece be b cm,
Then, b = (100 - X)/4 (since each side of the square formed is 1/4 of the original length)
Area of square formed from other piece = b^2 = ((100 - X)/4)^2 = (100 - X)^2/16 cm^2

The total area of the two squares is given as 325 cm^2, so:
X^2/16 + (100 - X)^2/16 = 325
X^2 + (100 - X)^2 = 325 * 16
X^2 + 10000 - 200X + X^2 = 5200
2X^2 - 200X + 10000 = 5200
2X^2 - 200X - 4800 = 0
X^2 - 100X - 2400 = 0
(X - 120)(X + 20) = 0
X = 120 or X = -20 (but lengths cannot be negative, so X = 120)

So, the length of one piece is 120 cm. The area of the square formed from this piece would be:
(120/4)^2 = (30)^2 = 900 cm^2

Therefore, the area of the square formed from the piece of length X cm is X^2/16 cm^2 or 900 cm^2 in this case.