Real-Life Math
You are an attorney operating a title-searching business in a rural area with lots of farmland. A local bank has asked you to perform a title search on a piece of farmland.
The property would be shaped like a rectangle, except for a triangle in the southwest corner that belongs to a neighboring farm. A fence runs along the boundary of the property, which is also the hypotenuse (the longest side) of the triangle.
When you search through the original land deed, you discover that the triangle-shaped patch of farmland legally belongs to the land you are title searching. The original deed describes a rectangular piece of land with a width of 2,000 yards and a length of 1,000 yards. The neighbor's fence is illegally placed on the property.
Before informing the bank of this fact, you decide to determine what percentage of land in the original deed is now being used by the neighbor. It will help the buyer decide whether the issue is worth fighting over in court. The total area of the property is 1,970,000 square yards.
You know that the length and width of the property you are title searching is 2,000 yards in the northern end, and 1,700 yards in the southern end. Also, the width of the property is 1,000 yards on the eastern end, and 800 yards on the western end.
What percentage of the original parcel of land is now part of the adjoining property?