Solving the Rectangle Area Problem: A Step-by-Step Guide for SEO

Optimizing content for SEO involves writing clear, comprehensive, and keyword-rich articles that are easy for search engines to understand and users to read. This article will walk you through a classic algebra problem—calculating the dimensions of a rectangle based on its area and the relationship between its length and width. We will also incorporate relevant keywords to ensure the content is optimized for search engines.

Problem Setup and Variables

We are given the area of a rectangle, which is 54 square centimeters, and we know that the width is 3 centimeters less than the length. Let's set up the problem using variables:

Considering the problem, the area A of the rectangle is given by:

A l × w

Since the area is 54 square centimeters:

l × w 54

We also know that the width is 3 centimeters less than the length:

w l - 3

Solving the Quadratic Equation

Now, let's substitute the expression for w into the area equation:

l × (l - 3) 54

This simplifies to:

l^2 - 3l - 54 0

To solve this quadratic equation, we can use the quadratic formula:

x frac{-b ± sqrt{b^2 - 4ac}}{2a}

Here, a 1, b -3, and c -54. Plugging these values into the formula gives:

l frac{-(-3) ± sqrt{(-3)^2 - 4 × 1 × (-54)}}{2 × 1}

This simplifies to:

l frac{3 ± sqrt{9 216}}{2}

l frac{3 ± sqrt{225}}{2}

l frac{3 ± 15}{2}

This gives us two possible solutions for l:

l frac{18}{2} 9

l frac{-12}{2} -6

Since the length cannot be negative, the valid solution is:

l 9 cm

Now, we can find the width:

w l - 3 9 - 3 6 cm

Conclusion

Thus, the dimensions of the rectangle are:

This problem-solving approach, combined with proper keyword usage, can help your SEO strategy. By incorporating relevant terms such as rectangle area and quadratic equation, the article becomes more attractive to search engines and more informative for readers.