Question

The 3 by 3 grid below shows nine 1 cm × 1 cm squares and uses 24 cm of wire. What length of wire is required for a similar 20 by 20 grid?

Answer 1

840

Explanation:

Hi there!

Usually, this kind of problem asks us the perimeter rather than the area. But when talking on this grid on how many cms are necessary to construct one made up of 9 squares 1cm x1 cm. We need to check one thing: Some line segments will be used twice. So this is not a classical perimeter question.

1) So we either manually and carefully count it avoiding not doing it twice the same common line segments.

Or.

2) By just applying an algorithm, Where n is the nxn grid

`n(n+1)+n(n+1)=Length \:of \:the \:wire`

So, for the 20x20 grid

`20(20+1)+20(20+1)=length\\\\20(21)+20(21)=length\\length=840 cm`