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Question 523457: The perimeter of a triangle is 48. The sides are the sum of three consecutive integers that are multiples of four. Find each side.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! The notion of three consecutive numbers that are divisible by 4 has to be interpreted. On the number, there is no instance where three consecutive numbers are divisible by 4. So it must mean that you are find three numbers that are multiples of 4 in sequence, but not really "consecutive" in the common meaning of the word "consecutive." So, we can define the three numbers a:
x = a number that, we hope, is divisible by 4
x + 4 = the next number that would be divisible by 4, given x is divisible by 4
x + 8 = the next number that would be divisible by 4, given x+4 is divisible by 4
.
x +(x+4) + (x+8) = 48
3x +12 = 48
3x = 36
x = 12
so
x+4 = 16
x+8 = 20
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12+16+20 = 48
.
Answer: The three numbers are 12, 16, and 20.
.
Done.
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