the base of a triangle is (c+2) ft and the area is (2c^3+16) ft^2. what is the height?
please help me i don't understand how to solve for the height.
The area of a triangle is always half the product of the base and height.
In this case the base :
b = c + 2
A = b * h / 2
A = ( c + 2 ) * h / 2
The area is ( 2 c ^ 3 + 16 ) so:
2 c ^ 3 + 16 = ( c + 2 ) * h / 2 Multiply both sides by 2
4 c ^ 3 + 32 = ( c + 2 ) * h Divide both sides by ( c + 2 )
( 4 c ^ 3 + 32 ) / ( c + 2 ) = h
h = ( 4 c ^ 3 + 32 ) / ( c + 2 )
After long division:
h = 4 c ^ 2 - 8 c + 16
h = 4 ( c ^ 2 - 2 c + 4 ) ft
To find the height of a triangle, we can use the formula for the area of a triangle, which is:
Area = (1/2) * base * height
In this case, the area is given as (2c^3 + 16) ft^2, and the base is given as (c + 2) ft. We need to solve for the height.
Let's substitute the given values into the formula:
(2c^3 + 16) = (1/2) * (c + 2) * height
Now, we can simplify the equation and solve for the height.
Multiply both sides of the equation by 2 to eliminate the fraction:
2 * (2c^3 + 16) = (c + 2) * height
Simplify:
4c^3 + 32 = (c + 2) * height
To isolate the height, divide both sides of the equation by (c + 2):
(4c^3 + 32) / (c + 2) = height
Now we have the height expressed in terms of c. Simply this expression cannot be simplified further.