SOLUTION: A 30 cm piece of wire is cut in two. Once piece is bent into the shape of a square and the other piece bent into the shape of a rectangle with 2:1 ratio. What are the lengths of th

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Question 887291: A 30 cm piece of wire is cut in two. Once piece is bent into the shape of a square and the other piece bent into the shape of a rectangle with 2:1 ratio. What are the lengths of the two pieces if the sum of the area of the square and the rectangle is a minimum?
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Two starting lengths from the wire, .

The square: x for one side length. Area is .

The rectangle: 2y to y may be the sides ratio. Area is .

If assign S as the sum of the areas, then .

Accounting for the sum of perimeters to be 30 is also needed.
Back with u and v,
and ----based on the given ratio of its dimensions.
and .

---THIS equation can be used to substitute for either x or y in the S equation. You can then determine the minimum value for S.

Maybe you can take the pathway to the solution described.

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