the width of a rectangle is increased by one tenth, but the area remains the same. by what fraction has the length of the rectangle been reduced?
original dimensions ---- w by l
original area = wl
new width = 9w/10
new length = L
L(9w/10) = lw
L = lw/(9w/10) = (10/9)l = 1.111..
so the length would have to increase, not be reduced, as your question stated.
The increase is 10/9 of the original or appr 11.1%
check:
if wl is the area, then
(9/10)w * (10/9)l = wl