SOLUTION: I can not figure out what in trapezoid WXYZ with bases ZY and WX, ZY= 12, YX= 10, WZ= 17, and ZD= 8. Find the length of base WX

Question 1138627: I can not figure out what in trapezoid WXYZ with bases ZY and WX, ZY= 12, YX= 10, WZ= 17, and ZD= 8. Find the length of base WX

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52867) (Show Source): You can put this solution on YOUR website!
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I can not figure out what in trapezoid WXYZ with bases ZY and WX, ZY= 12, YX= 10, WZ= 17, and ZD= 8. Find the length of base WX
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The point D is not defined in the problem, therefore, the solution is not possible.

Answer by greenestamps(13206) (Show Source): You can put this solution on YOUR website!

Please take the time to look at your post before you submit it. The trapezoid does not have a vertex D; there is no segment ZD. It is clear that you must mean ZX... but we shouldn't have to figure that out.

Here is a rough picture, approximately to scale....

Angles YZX and WXZ are congruent -- parallel lines WX and YZ cut by transversal ZX.

By the law of cosines in triangle XYZ,

By the law of cosines in triangle WXZ,

The quadratic expression does not factor; the quadratic formula gives us

which, to a few decimal places, is x = 16.552.

ANSWER: The length of base WX is approximately 16.552.

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