The Areas Of The Rectangles Are Given. Use Factoring To Find Expressions For The Missing Dimensions. SEE EXAMPLE 3 34. ? ? ? 9xy2 12x²y³​

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The Areas of Rectangles: Using Factoring to Find Missing Dimensions

In mathematics, the area of a rectangle is calculated by multiplying its length and width. When the area of a rectangle is given, we can use factoring to find expressions for the missing dimensions. In this article, we will explore how to use factoring to find the missing dimensions of a rectangle when its area is given.

What is Factoring?

Factoring is a mathematical process of expressing a polynomial as a product of simpler polynomials. It is a way of breaking down a complex expression into simpler components. In the context of finding missing dimensions of a rectangle, factoring can be used to express the area of the rectangle as a product of its length and width.

Example 1: Finding the Missing Dimension

Let's consider an example where the area of a rectangle is given as 9xy^2. We need to find the missing dimension, which is either the length or the width of the rectangle.

To find the missing dimension, we can start by factoring the given area:

9xy^2 = 3xy * 3xy

From this factorization, we can see that the missing dimension is 3xy.

Example 2: Finding the Missing Dimension

Let's consider another example where the area of a rectangle is given as 12x2y3. We need to find the missing dimension, which is either the length or the width of the rectangle.

To find the missing dimension, we can start by factoring the given area:

12x2y3 = 3x2y2 * 4xy

From this factorization, we can see that the missing dimension is 4xy.

Example 3: Finding the Missing Dimension

Let's consider an example where the area of a rectangle is given as 34. We need to find the missing dimension, which is either the length or the width of the rectangle.

To find the missing dimension, we can start by factoring the given area:

34 = 17 * 2

From this factorization, we can see that the missing dimension is 17 or 2.

In conclusion, factoring can be used to find expressions for the missing dimensions of a rectangle when its area is given. By breaking down the given area into simpler components, we can identify the missing dimension and express it as a product of simpler polynomials. This technique can be applied to a wide range of problems involving the areas of rectangles.

  • When factoring the given area, look for common factors that can be expressed as a product of simpler polynomials.
  • Use the distributive property to expand the factored expression and verify that it matches the given area.
  • Be careful when identifying the missing dimension, as it may be a product of multiple factors.
  • Failing to factor the given area completely, resulting in an incorrect expression for the missing dimension.
  • Identifying the wrong factor as the missing dimension.
  • Failing to verify that the factored expression matches the given area.

Factoring can be used in a wide range of real-world applications, including:

  • Geometry: Factoring can be used to find the missing dimensions of a rectangle when its area is given.
  • Algebra: Factoring can be used to solve equations and inequalities involving polynomials.
  • Calculus: Factoring can be used to find the derivative and integral of a function.
  1. Find the missing dimension of a rectangle with an area of 15x2y3.
  2. Find the missing dimension of a rectangle with an area of 24xy^2.
  3. Find the missing dimension of a rectangle with an area of 36.
  1. 5xy
  2. 6x
  3. 6
    The Areas of Rectangles: Using Factoring to Find Missing Dimensions - Q&A

In our previous article, we explored how to use factoring to find expressions for the missing dimensions of a rectangle when its area is given. In this article, we will answer some of the most frequently asked questions about factoring and finding missing dimensions.

Q: What is factoring, and how is it used to find missing dimensions?

A: Factoring is a mathematical process of expressing a polynomial as a product of simpler polynomials. It is a way of breaking down a complex expression into simpler components. In the context of finding missing dimensions of a rectangle, factoring can be used to express the area of the rectangle as a product of its length and width.

Q: How do I know which factor is the missing dimension?

A: When factoring the given area, look for common factors that can be expressed as a product of simpler polynomials. The missing dimension is usually a product of multiple factors. Use the distributive property to expand the factored expression and verify that it matches the given area.

Q: What if I have a rectangle with an area of 0? Can I still use factoring to find the missing dimension?

A: Yes, you can still use factoring to find the missing dimension, even if the area of the rectangle is 0. In this case, the factored expression will be a product of zero factors, which means that the missing dimension is also 0.

Q: Can I use factoring to find the missing dimension of a rectangle with a negative area?

A: No, you cannot use factoring to find the missing dimension of a rectangle with a negative area. The area of a rectangle cannot be negative, so it is not possible to find a missing dimension in this case.

Q: How do I know if I have factored the given area completely?

A: To verify that you have factored the given area completely, use the distributive property to expand the factored expression and verify that it matches the given area. If the factored expression does not match the given area, you may need to factor it further.

Q: Can I use factoring to find the missing dimension of a rectangle with a fractional area?

A: Yes, you can use factoring to find the missing dimension of a rectangle with a fractional area. In this case, the factored expression will be a product of fractions, and you will need to simplify the expression to find the missing dimension.

Q: What if I have a rectangle with an area that is a perfect square? Can I still use factoring to find the missing dimension?

A: Yes, you can still use factoring to find the missing dimension, even if the area of the rectangle is a perfect square. In this case, the factored expression will be a product of two identical factors, and you can use this to find the missing dimension.

Q: Can I use factoring to find the missing dimension of a rectangle with a variable area?

A: Yes, you can use factoring to find the missing dimension of a rectangle with a variable area. In this case, the factored expression will be a product of variables, and you will need to simplify the expression to find the missing dimension.

In conclusion, factoring can be a powerful tool for finding missing dimensions of rectangles. By understanding how to factor expressions and identify the missing dimension, you can solve a wide range of problems involving the areas of rectangles.

  • Always verify that the factored expression matches the given area.
  • Use the distributive property to expand the factored expression and simplify it.
  • Be careful when identifying the missing dimension, as it may be a product of multiple factors.
  • Failing to factor the given area completely, resulting in an incorrect expression for the missing dimension.
  • Identifying the wrong factor as the missing dimension.
  • Failing to verify that the factored expression matches the given area.

Factoring can be used in a wide range of real-world applications, including:

  • Geometry: Factoring can be used to find the missing dimensions of a rectangle when its area is given.
  • Algebra: Factoring can be used to solve equations and inequalities involving polynomials.
  • Calculus: Factoring can be used to find the derivative and integral of a function.
  1. Find the missing dimension of a rectangle with an area of 15x2y3.
  2. Find the missing dimension of a rectangle with an area of 24xy^2.
  3. Find the missing dimension of a rectangle with an area of 36.
  1. 5xy
  2. 6x
  3. 6