A string is cut into two parts such that the ratio of the lengths of the complete string and the smaller part is 40 times the ratio of the lengths of the smaller part and the larger part. Find the ratio of the length of the string and the square of the length of the smaller part (taken in cm) if the longer part is 8 cm.
Solution
Let the length of the smaller part be a cm and the length of the string be I cm
$\therefore $ Larger part = 4 cm
Given that, $\frac {I} {a} = \frac {40a}{8}$
$\Rightarrow I = 5a^2$
$\Rightarrow \frac {I}{a^2} = 5 : 1$