What is the area of this scalene triangle 12x 15x 9x
To find the area of a scalene triangle, we need two things: the base and the height. However, in the given triangle, we only have the side lengths.
To proceed, we can use Heron's formula to find the area. Heron's formula states that the area of a triangle whose sides have lengths a, b, and c can be calculated using the formula:
Area = √(s(s - a)(s - b)(s - c))
where s is the semiperimeter of the triangle given by:
s = (a + b + c)/2
In this case, the side lengths of the triangle are 12x, 15x, and 9x. We can substitute these values into Heron's formula to find the area.
First, calculate the semiperimeter (s):
s = (12x + 15x + 9x)/2
s = (36x)/2
s = 18x
Next, substitute the side lengths and the semiperimeter into the formula:
Area = √(18x(18x - 12x)(18x - 15x)(18x - 9x))
Area = √(18x(6x)(3x)(9x))
Area = √(18x * 6x * 3x * 9x)
Area = √(2916x^5)
Area = 54x^2√x
Therefore, the area of the given scalene triangle is 54x^2√x.