SOLUTION: The perimeter of a hexagon is 18x+5. Four sides have the following side lengths: 8x, 3x-2, x+3, 2x-3. Choose all the pairs that could be the missing two sides. a. 4x+2, x+5 b

Question 1035522: The perimeter of a hexagon is 18x+5. Four sides have the following side lengths: 8x, 3x-2, x+3, 2x-3.
Choose all the pairs that could be the missing two sides.
a. 4x+2, x+5
b. 2x, 2x+7
c. 5x-3, x+10
d. 3x-10, x+17
I tried adding 8x, 3x-2, x+3, and 2x-3 then subtracting that from 18x+5 then seeing if a,b,c or d would equal to the number but it doesn't, please help me.
Also on my homework this goes under the category of factoring, thank you.

Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
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The perimeter of a hexagon is 18x+5. Four sides have the following side lengths: 8x, 3x-2, x+3, 2x-3.
Choose all the pairs that could be the missing two sides.

a.  4x+2, x+5      <--- bad

b.  2x, 2x+7       <--- good

c.  5x-3, x+10     <--- bad

d.  3x-10, x+17    <--- good

The method:

Note that 8x + (3x-2) + (x+3) + (2x-3) = 14x - 2.

Thus two other addends should comlement 14x-2 to 18x+5.

It is easy to check that only options "b" and "d" satisfy this condition.

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