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Determine the smallest possible circumference of the triangle.?
An equilateral triangle has in centimeters the side lengths x + 2y, 5y - x and 3x - y where x and y are positive integers. Determine the smallest possible circumference of the triangle.
I thought ........
x+2y=5y-x=3x-y
2x=3y
x=1.5y
circumference of the triangle: (x+2y)+(5y-x)+(3x-y)
Then I do not know how I can solve thisproblem, I thought that maybe you could solve it with an equation system..... ???
But I dont know how. Can someone show me step by step because I want to learn. I only know that the answer is going to be 21cm.
1 Answer
- RayLv 74 months ago
Continuing where you left off:
circumference of the triangle = 6y + 3x
But x = 1.5y
Circumference of the triangle = 6y + 3(1.5y)
Circumference of the triangle = 10.5y
Now x and y have to be positive integers.
y cannot be the smallest positive integer because x would then be 1.5, but x also has to a positive integer.
Therefore the smallest possible value for y is 2.
When y is 2 the circumference is 21.
