Question

A piece of wire that is 200 ft long is to be cut into two pieces and each of the piece is to be bent into a square. How should the wire be cut if the area of one of the squares is 1000ft2 smaller than the other?

Answer 1

60 ft and 140 ft

Explanation:

Total length = 200 ft

Let the length of one piece is L and other is 200 - L.

`1000 + \left ((L)/(4) \right )^2 = \left ( (200 - L)/(4) \right )^2\\\\16000 +L^2 = 40000 + L^2 - 400 L\\\\L= 60 ft`

So, the length of the other piece is 140 ft.

Answer 2

Length of first cut = 140

Length of second cut = 60

Explanation:

Given:

Length of wire = 200

Find:

Length of each cut

Computation:

Assume;

Side of first square = x/4

Side of second square = [200 - x] / 4 = 50 - x/4

So,

[x/4]² - [50 - x/4]²

x²/16 - x²/16 - 2500 + 25x = 1000

- 2500 + 25x = 1000

25x = 3500

x = 140

Side of first square = 140/4

Side of first square = 35

Side of second square = 50 - 140/4

Side of second square = 15

Length of first cut = 4 x 35

Length of first cut = 140

Length of second cut = 200 - 140

Length of second cut = 60