SOLUTION: The parallel sides of a trapezoid are 12" and 18" long. The non-parallel sides meet when one is extended 9" and the other is extended 16". How long are the non-parallel sides of

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Question 149700: The parallel sides of a trapezoid are 12" and 18" long. The non-parallel sides meet when one is extended 9" and the other is extended 16". How long are the non-parallel sides of this trapezoid.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If we draw the picture, we get


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From the picture, we can see that there is one large triangle and there is one smaller triangle towards the top.

It turns out that these triangles are similar. So this means that these ratios hold:

12%2F18=9%2F%289%2Bx%29 and 12%2F18=16%2F%2816%2By%29


So let's find the length of x:

12%2F18=9%2F%289%2Bx%29 Start with the first ratio.


%2812%29%289%2Bx%29=%289%29%2818%29 Cross multiply


108%2B12x=162 Distribute and multiply.


12x=162-108 Subtract 108 from both sides.


12x=54 Combine like terms on the right side.


x=%2854%29%2F%2812%29 Divide both sides by 12 to isolate x.


x=4.5 Divide.


So the length of x is 4.5 units.

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Now let's find the length of y:

%2812%29%2F%2818%29=%2816%29%2F%2816%2By%29 Start with the second ratio


%2812%29%2816%2By%29=%2816%29%2818%29 Cross multiply


192%2B12y=288 Distribute and multiply.


12y=288-192 Subtract 192 from both sides.


12y=96 Combine like terms on the right side.


y=%2896%29%2F%2812%29 Divide both sides by 12 to isolate y.


y=8 Reduce.


So the length of y is 8 units.


So the lengths of the non-parallel sides are 4.5 and 8 units.