# algebra

One side of a triangle is 6 meters more than twice the shortest side. The perimeter is 75 meters. Find all three sides.

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1. let shortest side be x
then the described side is 2x+6
third side = y
x + 2x + 6 + y = 75
y = 69 - 3x

restrictions: the sum of any two sides must be greater than the third side
x + 2x+6 > 69-3x ---> 6x > 63 , x > 10.5
x + 69-3x > 2x+6 --->-4x > -63 , x < 15.75
69-3x + 2x+6 > x ---> -2x > 75 , x < -37.5, not possible

10.5 < x < 15.75

try x = 12
one side is 12, the second side is 30, the third side is 69-3(12) = 33

is 12+30>33 , yes
is 12+33> 30 , yes
is 33+30> 12 yes

try x = 14
one side is 14, the second side is 34, the third side is 69-3(14) = 27
is 14+34>27 , yes
is 14+27>34 , yes
is 27+34> 14, yes

as you can see there is an infinite number of solutions, as long as you the smallest side is between 10.5 and 15.75

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