Final answer:
To determine the base and height of the triangle, we denote the base as 'b', express the height as 'h = 2b - 3', and use the area formula 'A = 1/2 × base × height' with the given area of 7 m². We solve the resulting quadratic equation to find 'b', and then calculate 'h' accordingly.
Step-by-step explanation:
To solve the problem, we start by denoting the base of the triangle as b meters. According to the problem statement, the height (h) is three meters less than twice the base, which we can write as h = 2b - 3. We know the area (A) of a triangle is given by the formula A = 1/2 × base × height. Substituting the given area of 7 m² and the expression for h, we get:
7 = 1/2 × b × (2b - 3)
To find the value of the base, we solve this quadratic equation. Multiplying both sides by 2 to eliminate the fraction, we get:
14 = b × (2b - 3)
Expanding and rearranging gives us:
2b^2 - 3b - 14 = 0
Using the quadratic formula or factoring (if applicable), we can find the value of b. Once we have b, we can easily calculate h by substituting b into the h equation. Finally, we ensure that both base and height are positive, as they must be for a triangle's physical dimensions.