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I created this task with real world application in mind. My intention was to provided students with a problem based task that made them think. My students had been scaffolded with previous tasks dealing with perimeter and variables. Students fill out the missing parts in the diagram and then add all the sides together to find the total perimeter in terms of x. Students have to combine like terms, use the distributive property, and solve. I really liked this task because it incorporates perimeter and area as well. As an extension, I asked students to find the missing side lengths after finding a solution for x. Hope you enjoy!
Feel free to modify this or make it your own related to your own school.
Answer key - When you add all of the sides together you should get 43x -2
Then set 43x - 2 = 1, 718
x should be = to 40
Plug in 40 to find the area of the buildings as well as the missing side lengths