Question

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.

Answer 1

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