If you wanted to divide a right triangle into two equal parts (equal areas), how many different ways is this possible? Explain all your different solutions and any generalizations you can make.

Roger's Farm is a small corn and garden vegetable farm. Roger sells his produce at a local Farmer's Market. His field is in the shape of right triangle with the two legs of length 1295 feet and 405 feet, pictured below. He wants to divide his field into two equal areas by creating a dividing line parallel to AC. Divide the field according to these requirements. Prove that your solution is correct. What is the area in each of the two field sections? One section of the field will be planted in sweet corn. Search the Internet to find estimates for the yield of sweet corn. How much sweet corn can Roger produce?

Triangle ABC is a right triangle with being the right angle. Where should a line segment that is parallel to the base be located so that the right triangle is divided into two equal areas?

Roger's Market is a small fruit and vegetable stand off of Highway 218 just North of Cedar Falls. This year the owner wanted to divide his field, so he could grow equal areas of corn and garden vegetables. He could not figure out how to divide his field accurately. He showed me a sketch of his field that was a right triangle with the two legs 1295 feet and 405 feet respectively. He wanted to separate his field so that the dividing line was parallel to one of the legs. How should he divide the field?