Understanding the Problem
- 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 �=�2A=s2
Plugging in the given value: Each square has an area of �2s2 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×s2
Plugging in the given values: The total area for all eight pieces is 8�28s2 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:
5. Simplifying the Equation
To make the equation simpler, we can divide each side by 8:
This is the simplified quadratic equation Doug can use to find the side length, �s, of each piece of wood.