algebra

The area of a triangle is equal to 1/2 times its base times its height. Therefore, in order to solve for the length of the altitude, we need to set up the following equation: 1/2 × base × height = 6 square cm. Since the altitude has a length of 1/3 of the base, the equation can be rewritten as: 1/2 × base × 1/3base = 6 square cm. Simplifying the equation yields: base^2/6 = 6 square cm. Therefore, the length of the base is the square root of 36 cm, or 6 cm. Since the altitude is 1/3 the length of the base, then the length of the altitude is 6 cm divided by 3 cm, which is 2 cm. Therefore, the length of the altitude is 2 cm.