SOLUTION: A quadrilateral has sides 6 cm,10 cm,18 cm, and a cm. A quadrilateral similar to this, the corresponding sides are b,c, 36 cm, and 48 cm. Find a,b, and c.

Algebra ->  Polygons -> SOLUTION: A quadrilateral has sides 6 cm,10 cm,18 cm, and a cm. A quadrilateral similar to this, the corresponding sides are b,c, 36 cm, and 48 cm. Find a,b, and c.       Log On


   

Question 1107724: A quadrilateral has sides 6 cm,10 cm,18 cm, and a cm. A quadrilateral similar to this, the corresponding sides are b,c, 36 cm, and 48 cm. Find a,b, and c.
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39630) About Me  (Show Source):
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First Figure    6   10   18   a

Second Figure   b   c    36   48


system%2818%2F36=a%2F48%2C36%2F18=c%2F10%2C36%2F18=b%2F6%29
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Answer by Edwin McCravy(20064) About Me  (Show Source):
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Since 

1. the 18 cm. side of the first quadrilateral corresponds to the
   36 cm. side of the second quadrilateral.

2. the quadrilaterals are similar.

3. 18 cm is one-half of 36 cm and 36 cm is twice 18 cm,

therefore

every side of the first quadrilateral is half the side of the
corresponding side of the second quadrilateral.

and

every side of the second quadrilateral is twice the side of the
corresponding side of the first quadrilateral.

So:

I. The side of the second quadrilateral that measures b cm. corresponds 
to the side of the first quadrilateral that measures 6 cm., so b is
twice 6 cm. or 12 cm.   Answer: b = 12.


II. The side of the second quadrilateral that measures c cm. corresponds 
to the side of the first quadrilateral that measures 10 cm., so c is
twice 10 cm. or 20 cm.   Answer: c = 20.


III. The side of the second quadrilateral that measures 48 cm. corresponds 
to the side of the first quadrilateral that measures a cm., so a is
half of 48 cm. or 24 cm.   Answer: a = 24

Edwin