Which function rule can be used to represent the area of a triangle with a base b 8 in. longer than twice the height h in terms of the height?
a = bh/2
Since b = 2h+8,
a = (2h+8)h/2 = (h+4)h = h^2+4h
To represent the area of a triangle with the base b 8 in. longer than twice the height h in terms of the height, you can use the formula:
Area = (1/2) * base * height
Since the base is 8 inches longer than twice the height, we can write it as:
base = 2h + 8
Replacing the base in the formula, we get:
Area = (1/2) * (2h + 8) * h
Simplifying further:
Area = (h + 4) * h
Therefore, the function rule to represent the area of the triangle in terms of the height is:
Area = h^2 + 4h
To find the function rule that represents the area of a triangle, we need to recall the formula for the area of a triangle. The formula for the area of a triangle is given by the equation:
Area = (1/2) * base * height
In this case, the base of the triangle (b) is 8 inches longer than twice the height (h). So, we can write the base as:
b = 2h + 8
Now, substituting the value of the base into the area formula, we have:
Area = (1/2) * (2h + 8) * h
Simplifying further, we get:
Area = h * (2h + 8) / 2
So, the function rule that represents the area of a triangle in terms of the height is:
Area = (h * (2h + 8)) / 2