Pre calculus word problem

Question

The sum of the base and the height of the triangle is 18cm. Find the dimensions for which the area is a maximum. The triangle with maximum area has a height of _ cm? And a base of _ cm?

Answer 1

b represents the length of the base

18 - b represents the height

A = 0.5(b(18 - b))

A = -0.5b² + 9b

Maximum at b = 9 / 2(-0.5), or be = 9

What is the area?