Word Problems: Geometry Problems Solve each problem using a system of equations. Show all of your work, including labels for your variables. 1. Suppose you want to use 600 meters of fencing to surround two identical adjacent rectangular plots. Write a function for the combined area of the plots with respect to the length of one of the sides (x). What dimensions would produce the maximum combined area? What is that maximum combined area? 2. The area of a rectangle is 21 sq. ft. What are its dimensions if the length is 5 feet less than four times the width? 3. A farmer with 1000 meters of fencing wants to enclose a rectangular plot that borders along a straight river. If the farmer does not want to fence along the river, what is the largest area that can be enclosed? What dimensions produce that area? 4. The width of a rectangle is 2 less than half the length, and the area is 30. What is the perimeter of the rectangle? 5. A rectangular pen is constructed using one side of the house as a side of the pen. You have 100 feet of fencing for the other three sides. What dimensions would produce the maximum area? What is the maximum area? 6. A farmer wishes to enclose a rectangular field which will be partitioned into six smaller fields. If the farmer has only 10,000 meters of fencing available, what is the maximum combined area that can be enclosed? Write a function for the combined area of the plots with respect to the length of one of the sides (x). What dimensions produce the maximum combined area? 7. Suppose a stream borders our land, and we want to make a right-triangular garden with the stream as the hypotenuse. If we have only 80 feet of fencing, what is the maximum area of our garden? 8. You decide to build a dog run in a back corner your yard. If you only have 60 feet of fencing, what is the maximum area that you can enclose? What dimensions produce the maximum area?