A piece of length 1m is cut into two parts and each piece is bent to form a square. The total area of the two squares forms is 325cm. Given that one of the piece is x cm long,find the area of the square formed from this piece in terms of x.

Answer 1

Let the length of one piece be x cm, so the length of the other piece is (100-x) cm.

The area of the square formed from the piece of length x cm is x^2 cm^2.

The area of the square formed from the piece of length (100-x) cm is (100-x)^2 cm^2.

Given that the total area of the two squares is 325 cm^2, we have:

x^2 + (100-x)^2 = 325

Expanding this equation, we get:

x^2 + 10000 - 200x + x^2 = 325

2x^2 - 200x + 9975 = 0

Dividing by 2, we get:

x^2 - 100x + 4987.5 = 0

Using the quadratic formula, we find:

x = (100 +/- √(100^2 - 4*1*4987.5))/2

x = (100 +/- √(10000 - 19950))/2

x = (100 +/- √(-9950))/2

Since the square root of a negative number is not a real number, there are no real solutions to this equation. However, if we consider complex numbers, we have the solutions:

x = 50 + 49.8741 i

Therefore, the area of the square formed from the piece of length x cm is given by:

x^2 = (50 + 49.8741 i)^2 = 2500 + 2500 i + 2493.7104 i - 2451.99381

Area = 2493.7104 i + 48.00619