Question

A piece of length 1 metre is cut into two parts and each piece is bent to form a square .The total area of the two square forms is 325 square centimeters. Q1Give that one of the piece of x centimeter long ,find the area of the square formed from this piece in terms of x

Q2 Find the area of the square formed by the remaining piece in terms of x

Q3 Determine the possible values of x

Answer 1

[AI-generated answer — Bot GPT 3.5]

Q1: Let the length of one piece be x cm. Since the original piece was 1 metre (100cm) long, the length of the other piece is (100 - x) cm.

The area of a square is given by side x side. So, the area of the square formed by the piece of length x cm is x^2 square cm.

Q2: Similarly, the area of the square formed by the piece of length (100 - x) cm is (100-x)^2 square cm.

Q3: Since the total area of the two squares is 325 square cm, we can write the equation:
x^2 + (100 - x)^2 = 325

Expanding and simplifying:
x^2 + 10000 -200x + x^2 = 325
2x^2 - 200x + 9715 = 0

Solving this quadratic equation for x using the quadratic formula:
x = [200 ± sqrt((200)^2 - 4(2)(9715))] / 2(2)
x = [200 ± sqrt(40000 - 38860)] / 4
x = [200 ± sqrt(1140)] / 4
x = [200 ± 33.77] / 4

So, the possible values of x are:
x = (200 + 33.77) / 4 = 58.43
or
x = (200 - 33.77) / 4 = 41.57

Therefore, the possible values of x are approximately 41.57 cm and 58.43 cm.