Final answer:
The base of the triangular sail is 4 meters and the height is 8 meters.
Step-by-step explanation:
Let the height of the triangular sail be h meters. According to the given information, the base of the sail is 4 meters shorter than its height, so the base can be represented as h - 4 meters.
The area of the triangular sail is given as 16 m². The formula to find the area of a triangle is A = (1/2) * base * height. Substituting the values, we have 16 = (1/2) * (h - 4) * h.
By simplifying the equation, we get h² - 4h - 16 = 0. Factoring this quadratic equation, we have (h - 8)(h + 2) = 0. Hence, the possible values for h are 8 and -2. However, the height cannot be negative, so h = 8.
Therefore, the base of the sail is h - 4 = 8 - 4 = 4 meters, and the height is h = 8 meters.
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