If the length of a rectangle increases by 10%, by what percentage should the breadth decrease to keep the area the same?

The breadth should fall by about 9.11%.

Area stays fixed, so length x breadth is constant.

New length = 1.1 times the old length.

New breadth = old breadth / 1.1 = 0.909 times the old.

Reduction = 1 - 1/1.1 = 0.0909, about 9.11%.

So the breadth is reduced by about 9.11%.