A wire of length 20m is to be cut into two pieces. One of the places will be bent into shape of a square and the other shape of an equilateral triangle. Where the wire should be cut so that the sum of the areas of the square and triangle is minimum?

Explanation

To solve the problem, we need to minimize the sum of the areas of a square and an equilateral triangle formed from a wire of length 20 meters. Let's break down the solution step by step.

### Step 1: Define Variables
Let the length of the wire used for the square be \( x \) meters. Therefore, the length of the wire used for the equilateral triangle will be \( 20 - x \) meters.

### Step 2: Area of the Square
The perimeter of the square is equal to \( x \). Since the perimeter of a square is \( 4 \times \text{side} \), the side length of the square can be expressed as:
\[
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