Answer:
48 = 1/2 * b * (b - 4)
b
Explanation:
According to the problem, the height of the triangle is 4m less than the base. We can express this mathematically as:
height = b - 4
The area of a triangle is given by the formula:
area = 1/2 * base * height
Substituting the given values, we get:
48 = 1/2 * b * (b - 4)
Simplifying the equation:
96 = b^2 - 4b
Rearranging and setting the equation equal to zero:
b^2 - 4b - 96 = 0
We can solve for b using the quadratic formula:
b = (-(-4) ± sqrt((-4)^2 - 4(1)(-96))) / (2(1))
b = (4 ± sqrt(16 + 384)) / 2
b = (4 ± 20) / 2
We take the positive root since the base of a triangle cannot be negative:
b = (4 + 20) / 2
b = 12
Therefore, the length of the base is 12 meters.
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