Differentiation application

Question

 a straight piece of wife is 28 cm. It is cut into two pieces. One pieces is bent into a square and the other is bent into a rectangle whose width is 3 times the height. What are the dimensions of the square and rectangle that minimize the sum of the areas 

Answer 1

I feel like this is missing information. We do not know the length of each wire. The square is the most efficient shape, but we want inefficiency here since it's asking to minimize area. Because of this, the rectangle will use almost the entire length of the wire with a perimeter of ~27.999cm, and the square will be infinitely small.

 

We can effectively say that the rectangle has a perimeter of 28cm.

 

Equations:

P=2h+2w

A=hw

w=3h

 

P=2h+2w

(28cm)=2h+2(3h)

(28cm)=8h

3.5cm=h

 

w=3h

w=3(3.5cm)

w=10.5cm

 

A=hw

A=(3.5cm)(10.5cm)

A=36.75cm²

 

Since we still need to account for the square, the dimensions are really like 3.4449cm x 10.449cm. The square will be infinitely small like. 0.00001cm x 0.00001cm.