A magic rectangular belt always shrinks its length to 1/2 and width to 1/3 whenever its owner wishes something. after three such wishes, its surface was 4 cm2. what was the original length, if the original width was 9 cm ?
Answers
Answered by
4
Let the original length be l and the original width is 9 cm.
After 1 wish, new length = l*1/2 and new width = 9*1/3
After 3 wishes, final length = l*1/2*1/2*1/2 and final width = 9*1/3*1/3*1/3
Now, final length * final width = 4
So, l*1/2*1/2*1/2 * 9*1/3*1/3*1/3 = 4
or, l/8 * 9/27 = 4
or, l/24 = 4
Thus original length = l = 24*4 = 96 cm.
After 1 wish, new length = l*1/2 and new width = 9*1/3
After 3 wishes, final length = l*1/2*1/2*1/2 and final width = 9*1/3*1/3*1/3
Now, final length * final width = 4
So, l*1/2*1/2*1/2 * 9*1/3*1/3*1/3 = 4
or, l/8 * 9/27 = 4
or, l/24 = 4
Thus original length = l = 24*4 = 96 cm.
Similar questions