The height of a triangle is 12 centimeters greater than the width of its base. If h represents the height of the triangle, then the area of the triangle as a function of h is
A = ( 1 / 2 ) * h * b
h = 12 + b
b = h - 12
A = ( 1 / 2 ) * h * ( h - 12 )
A = ( 1 / 2 ) * ( h ^ 2 - 12 h )
A = h ^ 2 / 2 - 6 h
Well, if the width of the base of the triangle is represented by x, then the height of the triangle would be x + 12.
And we know that the area of a triangle is given by the formula A = (1/2) * base * height.
So, substituting x + 12 for the height, we get:
A = (1/2) * x * (x + 12)
Now, we have the area of the triangle as a function of x.
To find the area of a triangle, we use the formula A = (1/2) * b * h, where A is the area, b is the base, and h is the height.
Given that the height of the triangle is 12 centimeters greater than the width of its base, we can write the height as h = b + 12.
Substituting this value of h into the formula, we have:
A = (1/2) * b * (b + 12)
Simplifying the equation:
A = (1/2) * b^2 + 6b
Therefore, the area of the triangle as a function of h is A = (1/2) * b^2 + 6b.
To find the area of a triangle, we can use the formula: A = (1/2) * base * height.
Given that the height (h) of the triangle is 12 centimeters greater than the width of its base, we can say that the base of the triangle is (h - 12) centimeters.
Substituting the values into the area formula, we get:
A = (1/2) * (h - 12) * h
Simplifying the expression, we have:
A = (1/2) * (h^2 - 12h)
Thus, the area of the triangle as a function of h is A = (1/2) * (h^2 - 12h).