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

Algebra ->  Parallelograms -> 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       Log On


   

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(52866) About Me  (Show Source):
You can put this solution on YOUR website!
.

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) About Me  (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,

10%5E2+=+8%5E2%2B12%5E2-2%2A8%2A12%2Acos%28theta%29

cos%28theta%29+=+108%2F192+=+9%2F16

By the law of cosines in triangle WXZ,

17%5E2+=+x%5E2%2B8%5E2-2%2Ax%2A8%2Acos%28theta%29
189+=+x%5E2%2B64-16x%289%2F16%29
x%5E2-9x-125+=+0

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

x+=+%289+%2B+sqrt%2881%2B500%29%29%2F2

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

ANSWER: The length of base WX is approximately 16.552.