A six by eight grid is constructed with 48 small squares in a rectangle, as illustrated. If the diagonal of one of the small squares is 6 cm, what is the length of the diagonal \(\bar{AC}\)?
A _________8_________ D


6 


B ___________________ C
Thanks!
We can construct the following rectangle ABCD with squares of side 1
The length of the diagonal of one of these squares = √[1^2 + 1^2] = √2
And the diagonal AC of the image = √[6^2 + 8^2] = √100 = 10
Since these are similar figures, we can solve for the diagonal length of your problem, AC, thusly
6 / √2 = AC / 10 crossmultiply
10*6 / √2 = AC = 60/√2 = 60√2/ 2 = 30√2