Final answer:
After solving the quadratic equation derived from the area formula for a triangle, neither the calculated base and height of 6 m and 13 m, nor the provided options (A, B, C, D) with various base and height measurements result in an area of 39 m² for the triangular sail, indicating a discrepancy in the provided information or a need for a recalculation.
Step-by-step explanation:
The question revolves around finding the base and height of a triangular sail given that the area is 39 m² and the base is 7 m shorter than its height. To solve for the base and height, one can use the formula for the area of a triangle, which is 1/2 × base × height.
Let the height of the triangle be h meters. Thus, the base will be h - 7 meters. Given the area of the triangle is 39 m², setup the equation:
½ × (h - 7) × h = 39
Multiplying through by 2 gives:
(h - 7) × h = 78
Expanding the left side we have:
h² - 7h - 78 = 0
This quadratic equation can be solved for h. Factorizing the quadratic equation, we find that (h - 13)(h - 6) = 0, providing the values h = 13 and h = 6. Since the base must be 7 m shorter than the height, we discard h = 6 as this would yield a negative base. Therefore, the height is 13 m and the base is (13 - 7) = 6 m. However, there seems to be a mistake because none of the provided options matches these dimensions, and also because the calculated area with these dimensions would be 39 m², which is not the correct area for a triangular sail as claimed.
It is important to check the provided options and calculations for discrepancies. If you find such errors, it's essential to review your work or inform the student about the mistake.