The length of one of the equal legs of an isosceles triangle is 8 cm less than 4 times the length of the base. If the perimeter is 29 cm, find the length of one of the equal legs.

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Lets say that the base of the triangle is x cm long.  Then the length of one of the equal legs is 4x - 8 (8 less than 4 times the length of the base.  The perimeter is the sum of the lengths of each side, and so:         leg + leg + base = perimeter(4x - 8) + (4x - 8) + x = 29  ...substitute the values     4x - 8 + 4x - 8 + x = 29  ...combine like terms                        9x -16 = 29  ...add 16 to both sides                              9x = 45  ...divide both sides by 9                                x = 5cmDon't forget that x is the base, and we need the length of one of the legs.  Again, the legs are (4x - 8)cm long.  Knowing now that x = 5, we can substitute and solve:length of leg = 4x - 8                     = 4(5) - 8                     = 20 - 8                     = 12cm