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can u find its length and its width only with the area of 144 square meters with the factoring method

In the provided image, the dimensions of the rectangle are expressed in terms of \( x \) and \( x + 8 \), where:

- The width is \( x \),
- The length is \( x + 8 \).

You want to find \( x \) and \( x + 8 \), given that the area of the rectangle is 144 square meters. The area \( A \) of a rectangle is calculated by multiplying its length and width, so we have:

\[
A = \text{length} \times \text{width}
\]

Substituting the given expressions for the length and width:

\[
144 = x(x + 8)
\]

Simplifying this:

\[
144 = x^2 + 8x
\]

Now, we rearrange this equation into standard quadratic form:

\[
x^2 + 8x - 144 = 0
\]

We'll solve this quadratic equation using factoring. First, we need to find two numbers that multiply to give \(-144\) and add to give \(8\). The numbers \(12\) and \(-12\) satisfy this, so we factor the quadratic as follows:

\[
x^2 + 8x - 144 = (x - 12)(x + 12) = 0
\]

Thus, we have two solutions for \( x \):

\[
x = 12 \quad \text{or} \quad x = -12
\]

Since \( x \) represents the width of a rectangle, it must be positive, so:

\[
x = 12
\]

Now that we have \( x = 12 \), we can find the length:

\[
\text{Length} = x + 8 = 12 + 8 = 20
\]

Therefore, the dimensions of the rectangle are:

- Width: \( 12 \) meters
- Length: \( 20 \) meters

Would you like further details or have any additional questions?

Here are 5 related questions for further practice:
1. How would you solve the same problem if the area was given as 200 square meters?
2. Can you use the quadratic formula to solve \( x^2 + 8x - 144 = 0 \) instead of factoring?
3. What are the units of measurement for area, length, and width in this context?
4. How would the dimensions change if the length was increased by 5 units?
5. What would happen to the area if the length and width were both doubled?

**Tip:** Factoring is a faster method to solve quadratics if the numbers are manageable. For more complex cases, try using the quadratic formula.

Can you find its length and its width only with the area of 144 square meters using the factoring method?

Learn how to find the dimensions of a rectangle using factoring when the area is given as 144 square meters. This problem involves key algebraic concepts such as quadratic equations and factoring, and is suitable for students in Grades 8-10.

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