Question

An isosceles triangle has a perimeter of 9y-15m.what is the length of each of the two equal sides, if the third sides is 3y-7

Answer 1

let each of the equal sides be x
then:
x + x + 3y-7 = 9y - 15
2x = 6y - 8
x = 3y - 4

but the sum of any two sides of a triangle must be greater than the 3rd side.
2x > 3y - 7 , x + 3y - 7 > x
2x +7 > 3y and 3y > 7
y < (2x+7)/3 and y > 7/3

no unique solution:
e.g. let y = 3, then x = 5, sides are 5, 5, 2
let y = 4, then x = 8 , sides are 8, 8, 5
let y = 5, then x = 11 sides are 11, 11, 8
let y = 6, then x = 14, sides are 14, 14, 11
..
let y = 20 , then x = 56, sides are 56, 56, 53

notice that the base is always 3 units less than each of the equal sides, and eventually the triangle will approach the shape of an equilateral triangle.
e.g let y = 5000 , then x = 14996, sides are 14996, 14996, and 14993