Question

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.Fid the area of the square formed by the remaining piece in terms of X

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let x be the length of the first piece and 1-x be the length of the second piece.

The area of the square formed by the first piece is (x/4)^2 = x^2/16.
The area of the square formed by the second piece is ((1-x)/4)^2 = (1-x)^2/16.

The total area of the two squares is x^2/16 + (1-x)^2/16 = (x^2 + 1 - 2x + x^2)/16 = 2x^2 - 2x + 1 / 16 = 325 cm^2.

Solving for x, we get:
2x^2 - 2x + 1 = 325 * 16
2x^2 - 2x + 1 = 5200
2x^2 - 2x - 5199 = 0
(2x + 77)(x - 67) = 0
x = 67

The area of the square formed by the remaining piece is (1-67)/4)^2 = 33/4)^2 = 1089/16 = 1089cm^2

Therefore, the area of the square formed by the remaining piece is 1089 cm^2.