Kabir divides a rectangle ABCD into eight non-overlapping squares as shown below. Find the ratio of AB to AD.
I started with the inner most square and called that side $a_1$. Then the sides of the second biggest square I called $a_2$. Then
$a_1+a_2=a_3$
$a_1+a_3=a_4$
$a_1+a_4=a+5$
What can I do now?
Best Answer
If you set the side of smallest square as $a$, and second smallest square as $b$, you will complete the length of side of all square:
To find that $a+2b = 8a-2b$ and so $4b = 7a$. This concludes $$AB:AD=(5a+2b):(7a+b)=34:35$$