Answer:
To solve this problem, we can use the formula for the area of a triangle, which is A=1/2bh, where b is the base and h is the height. In this problem, we are given that the area of the triangle is 128 square centimeters, so we can set up the following equation:
A = 1/2bh
128 = 1/2bh
We are also given that the height of the triangle is 8 centimeters greater than three times the base, so we can set up the following equation:
h = 3b + 8
We can substitute the second equation into the first equation to get the following:
128 = 1/2bh
128 = 1/2(3b + 8)b
128 = 3/2b^2 + 4b
We can then use the quadratic formula to solve for b, the base of the triangle:
b = (-4 +/- sqrt(4^2 - 4(3/2)(128)))/(2(3/2))
b = (-4 +/- sqrt(64 - 192))/3
b = (-4 +/- sqrt(-128))/3
Since the square root of a negative number is not a real number, we know that there is no solution to this equation, which means that the given information is not sufficient to determine the base of the triangle.
Therefore, the correct answer is that the base of the triangle cannot be determined from the information given.
To solve this problem, we can use the formula for the area of a triangle, which is A=1/2bh, where b is the base and h is the height. In this problem, we are given that the area of the triangle is 128 square centimeters, so we can set up the following equation:
A = 1/2bh
128 = 1/2bh
We are also given that the height of the triangle is 8 centimeters greater than three times the base, so we can set up the following equation:
h = 3b + 8
We can substitute the second equation into the first equation to get the following:
128 = 1/2bh
128 = 1/2(3b + 8)b
128 = 3/2b^2 + 4b
We can then use the quadratic formula to solve for b, the base of the triangle:
b = (-4 +/- sqrt(4^2 - 4(3/2)(128)))/(2(3/2))
b = (-4 +/- sqrt(64 - 192))/3
b = (-4 +/- sqrt(-128))/3
Since the square root of a negative number is not a real number, we know that there is no solution to this equation, which means that the given information is not sufficient to determine the base of the triangle.
Therefore, the correct answer is that the base of the triangle cannot be determined from the information given.