Math Problem Statement

Suppose you have two x^2 tiles and nine x tiles. How many one-tile squares would you need so that you could form a rectangle? State the area and dimensions of the rectangle.

Solution

The problem in the image asks the following:


Problem: You have the following tiles:

  • Two x2x^2-tiles
  • Nine xx-tiles

How many one-tile squares would you need to form a rectangle? State the area and dimensions of the rectangle.


To solve this:

  1. The total area of the tiles is the sum of the areas of the given tiles.

    • The two x2x^2-tiles contribute 2x22x^2 in total.
    • The nine xx-tiles contribute 9x9x in total.
    • Let’s say the number of one-tile squares you need is CC, and each one-tile square has an area of 1. So their total contribution to the area will be CC.
  2. The total area formed must equal the area of the rectangle, which will be expressed as Length×Width\text{Length} \times \text{Width}.

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