[Verified] Doug has 8 square pieces of wood. Each piece of wood has a side length of s centimeters. The total area of all eight pieces of wood is 200 square centimeters. Create a quadratic equation Doung can use to find the side length of each piece of wood.

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 �=�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:

8�2=2008s2=200

5. Simplifying the Equation

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

�2=2008s2=8200​ �2=25s2=25

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

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