Final answer:
The length of the base of the triangle is 5m and the height is 7m.
Step-by-step explanation:
In this problem, we are given that the height of a triangle is 2m more than the base, and the area of the triangle is 17.5 m².
Let's represent the base as 'b', and the height as 'h'.
According to the given information, the height is 2m more than the base, so we can write h = b + 2.
The formula for the area of a triangle is 1/2 × base × height.
Substituting the given values, we have 17.5 = 1/2 × b × (b+2).
To solve for 'b', we can multiply both sides of the equation by 2 to get rid of the fraction, resulting in 35 = b × (b+2).
Expanding this equation, we get b² + 2b = 35.
This is a quadratic equation that can be solved by factoring or using the quadratic formula.
By factoring, we have (b+7)(b-5) = 0. So, b = -7 or b = 5.
Since we can't have a negative base length, we take b = 5.
Therefore, the length of the base is 5m and the height is 7m (b+2).
Therefore, the base is 5m and the height is 7m.