What is the area of the region bounded by the three lines with equations 2x + y = 8, 2x - 5y = 20 and x + y = 12?

 Dec 17, 2020

Okay, so let's start by graphing the lines (use https://www.desmos.com/calculator for this). Then, you should see a triangle that is inside all three of the lines. One unfortunate thing you will notice is that the triangle is not a right triangle so you can't count the units in order to find the base and height :(. But of course, there still is a way to find the area of the triangle. Draw a rectangle where each vertice of the triangle is touching one of the sides/vertices of the rectangle. Then, you should end up with a few right triangles around the triangle you are trying to find the area of. Find the areas of those triangles and add them up, and subtract that sum from the area of the rectangle you drew. The answer would be the area of the region bounded by those equations. (Sorry if this was a bit unclear...I wasn't able to upload an image of the graph I made.)

Hope this helped!!

 Dec 17, 2020

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