Final answer:
To find the base and height of the triangular sail, we can use the area formula of a triangle.
Step-by-step explanation:
Let's assume that the height of the triangular sail is h meters. According to the given information, the base is 10 meters shorter than the height, so the base can be represented as h - 10. The area of a triangle is given by the formula 1/2 × base × height. Substituting the given values, we get:
1/2 × (h - 10) × h = 72
Multiplying through by 2:
h2 - 10h = 144
Arranging the equation:
h2 - 10h - 144 = 0
This is a quadratic equation. By factoring or using the quadratic formula, we can find the values of h that satisfy this equation.
Once we find the value of h, we can substitute it back into the expression for the base (h - 10) to find the base of the sail.