## Understanding the Problem

**Given**:

- Doug has 8 square pieces of wood.
- Each square piece has a side length of �
*s*centimeters. - The total area of all eight pieces is 200 square centimeters.

**Objective**: Find a quadratic equation to determine the side length, �*s*, of each square piece of wood.

## 2. Calculating Area of a Single Square Piece

### Formula for the Area of a Square:

Area=side length×side lengthArea=side length×side length �=�×�*A*=*s*×*s* �=�2*A*=*s*2

Plugging in the given value: Each square has an area of �2*s*2 square centimeters.

## 3. Calculating Total Area of All Square Pieces

### Formula for Total Area of 8 Pieces:

Total Area=Number of pieces×Area of each pieceTotal Area=Number of pieces×Area of each piece Total Area=8×�2Total Area=8×*s*2

Plugging in the given values: The total area for all eight pieces is 8�28*s*2 square centimeters.

## 4. Setting Up the Quadratic Equation

Given that the total area of all eight pieces is 200 square centimeters, we can set up the following equation:

8�2=2008*s*2=200

## 5. Simplifying the Equation

To make the equation simpler, we can divide each side by 8:

�2=2008*s*2=8200 �2=25*s*2=25

This is the simplified quadratic equation Doug can use to find the side length, �*s*, of each piece of wood.