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A piece of wire 100 cm long is to be cut into two pieces, each to be bent to make a square. The area of one square is to be 144cm^2 greater than that of the other. How should the wire be cut?

User Diginoise
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1 Answer

5 votes

Answer: 61.52 cm and 38.48 cm

Explanation:

A 100 cm wire is going to be cut into two pieces (A and B) and transformed into squares. To facilitate calculations, we can say that

A = 4x and B = 4y

as A + B = 100

4x + 4y = 100

Piece A, with a perimeter of 4x, is a square of x as a side and x² as area.

Piece B, with a perimeter of 4y, is a square of y as a side and y² as area.

We know that x² + 144 = y² → x² - y² = 144

4x + 4y = 100 → x + y = 25 (1)

x² - y² = 144 → (x-y)(x+y)=144 (2)

Substituting (1) in (2)

(x-y) . 25 = 144

(x-y) = 144/ 25

x - y = 5.76

Resolving the system:

x + y = 25

x - y = 5.76

__________________

2x = 30.76

x = 15.38

So A = 4x = 4 . 15.38 = 61.52

B = 100 - 61.52 = 38.48

User Andrei U
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