Let’s derive the quadratic equation step by step.
Finding the Quadratic Equation for the Area of Square Pieces of Wood
Concept Used: Area of a Square
The formula to find the area of a square is: Area=side length2Area=side length2
1. Determine the Area of One Square Piece
Given that the side length of each square piece of wood is �s centimeters, the area of one square piece is: Area of one piece=�2Area of one piece=s2
2. Determine the Total Area of All Eight Pieces
Since Doug has 8 pieces, the total area for all eight pieces is: Total Area=8×�2Total Area=8×s2
3. Set Up the Equation
Given that the total area of all eight pieces is 200 square centimeters, we can set up the equation as: 8�2=2008s2=200
This is the quadratic equation Doug can use to find the side length �s of each piece of wood.