Thread: Maximum & Minimum Problems

I am having some issues with these problems.
1. A farmer constructing a rectangluar fenced area with 420 meters of fencing. Calculate the dimensions that will yield the maximum area?

2. The sum of the base and height measures of a triangle is 15cm. What base height will generate the maximum area of the triangle?

I am not understanding how you begin to write the formula that allows to to get to the complete the square stage.

Originally Posted by Kat.T

I am having some issues with these problems.
1. A farmer constructing a rectangluar fenced area with 420 meters of fencing. Calculate the dimensions that will yield the maximum area?

I am not understanding how you begin to write the formula that allows to to get to the complete the square stage.

Perimeter = 420 = 2x + 2y. Therefore y = 210 - x.

Area = xy = x (210 - x).

A = x(210 - x) is a parabola. Use what you've been taught to find it's turning point.

Originally Posted by Kat.T

2. The sum of the base and height measures of a triangle is 15cm. What base height will generate the maximum area of the triangle?

I am not understanding how you begin to write the formula that allows to to get to the complete the square stage.

b + h = 15 => b = 15 - h.

A = bh/2 = (15 - h)h/2.

A = (15 - h)h/2 is a parabola. Use what you've been taught to find it's turning point.