Write a function rule for the area of a triangle whose base is 4ft more than the height. How does the area of the triangle change as the height changes? Explain

Question

My teacher wants me to find the equation in the word problem and to explain how the area changes if the height is also changed. But im stuck on the equation part.

Answer 1

h = height and b = base and A = area

 

b = h + 4

and

A =(1/2)bh = (1/2)h(h+4) = (1/2)(h² + 4h)

 

If h increases by s, then the new area = (1/2)(h + s)(h + s +4) = (1/2)(h² + 2hs + s² + 4h + 4s)

The increase in area is then found by subtraction to be

(1/2)[(2h + 4)s + s²]

 

If this question was asked in a calculus or pre-calculus class, then this is a prelude to questions of related rates.

 

I hope this helps, but if not, please send me a message.