If on the Trial Balance, "Cottages" is debited $125000, and Furniture, debited, 26,000, and I am ask to find the annual depreciation if the annual depreciation is $6000 on cottages and $2400 on furniture,how do I estimate the useful life of them both?

The formula for getting the annual depreciation in a straight line method is Acquisition Cost minus the Salvage Value then divide by the Estimated Life. Since your problem has no salvage value then just divide the Acquisition Cost with the Annual Depreciation to get the useful life which is 20.83 for the Cottages and 10.83 for the Furniture.