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March 10th, 2015, 06:54 PM  #1 
Senior Member Joined: Nov 2013 Posts: 247 Thanks: 2  Base length of trapezoid given area, height, and nonparallel side lengths
Let's suppose that we have a trapezoid that has an area of 164 square units. The nonparallel side lengths are 10 units and 17 units. The height is 8 units. Given this data, how would I find the length of the smaller parallel side? Last edited by skipjack; March 10th, 2015 at 11:45 PM. 
March 10th, 2015, 07:32 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,880 Thanks: 1503 
Have you made a sketch? If so, you can take advantage of two right triangles whose sides are Pythagorean triples ... x = smaller parallel base length x + 6 + 15 = larger parallel base length 4(2x + 21) = 164 Solve for x 
March 11th, 2015, 08:31 AM  #3 
Senior Member Joined: Nov 2013 Posts: 247 Thanks: 2 
4(2x+21) = 164 4x+84=164 4x=80 x=20 So the length of the smaller parallel side is 20 units. 
March 11th, 2015, 08:58 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,880 Thanks: 1503  

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area, base, height, length, lengths, nonparallel, nonparallel, side, trapezoid 
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