# math

The base of the triangle is 17. The other two sides are integers and one of the sides is twice as long as the other. What is the longest possible length of the side of the triangle.

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1. shorter of the other sides --- x
longer of the other sides ---- 2x

To be a triangle the sum of any two sides must be greater than the third side

x+2x > 17 AND x+17>2x AND 2x+17>x
3x > 17 AND x < 17 AND x > -17
x > 17/3 AND x < 17
(x is between 5.666.. and 17)

the largest value of x we could have is 16
so the largest side can be 32

triangle is 16 by 17 by 32

check:
is 16+17>32 ? yes
is 16+32>17 ? yes
is 32+17>16 ? yes

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