Question

a 75m long piece of wire is cut into parts, one being 30m long. if each part is bent to form a square, what is the ratio of the area of the larger square to the smaller square? please no copy paste from google

Answer 1

Answer:

Let the length of the first piece of wire be x The second piece is of length 30-x.

The sides of the square formed by the first wire is x/4, so its area is x²/16 square centimetres.

Similarly, the area of the second square is (30-x)²/16

So if we call the total area y, we have y as a function of x

y = x²/16 + (30-x)²/16

We can simplify this y = (2x² - 60x + 900)/16

You can then use a graphical method to find the minimum and maximum. Or differentiate.

An easier method will be to consider symmetry. The answer must be (by symmetry) either x = 0 or x = 15. So you calculate the total area with these two values and you find that x = 15 gives the smallest total area