# math

an isosceles triangle has perimeter of 15m. Find all integral possibilities for the lengths of the side in meters. Hint: the sum of the lengths of any two sides of a triangle must exceed the third side.

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1. let each of the equal sides be x
let the third side by y

2x + y = 15
y = 15-2x , clearly 15-2x >0 ----> x < 7.5 **
also x+x > y ----> y < 2x
x+y > x ----> y > 0 ----------> 0 < y < 2x ***
form a table of values satisfying both ** and ***
x y
7 1 yes
6 3 yes
5 5 yes
4 7 yes
3 9 NO

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