My Math Forum Base length of trapezoid given area, height, and non-parallel side lengths

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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 non-parallel side lengths Let's suppose that we have a trapezoid that has an area of 164 square units. The non-parallel 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
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Quote:
 Originally Posted by caters 4(2x+21) = 164 4x+84=164 4x=80 x=20 So the length of the smaller parallel side is 20 units.
$4(2x+21) \ne 4x+84$

try again ...

 Tags area, base, height, length, lengths, non-parallel, nonparallel, side, trapezoid

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