Math Problem Statement
Solution
The problem in the image asks the following:
Problem: You have the following tiles:
- Two -tiles
- Nine -tiles
How many one-tile squares would you need to form a rectangle? State the area and dimensions of the rectangle.
To solve this:
-
The total area of the tiles is the sum of the areas of the given tiles.
- The two -tiles contribute in total.
- The nine -tiles contribute in total.
- Let’s say the number of one-tile squares you need is , and each one-tile square has an area of 1. So their total contribution to the area will be .
-
The total area formed must equal the area of the rectangle, which will be expressed as .
To proceed:
- We need to form a quadratic equation by expressing the area as a factorable expression (the product of length and width).
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Area Calculation
Formulas
Area of a rectangle = length x width
Quadratic Equations
Theorems
Factoring Quadratic Equations
Suitable Grade Level
High School
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