A rectangks length is 3 tines its width, w. It's arca is 243 square units. Which equation can be used to find the with of the rectangle!

Given that the length of the rectangle is 3 times its width and the area of the rectangle is 243 square units, we can use the formula for the area of a rectangle:

\[
\text{Area} = \text{Length} \times \text{Width}
\]

Let's define:
- \( w \) as the width of the rectangle.
- The length \( L = 3w \) (since the length is 3 times the width).

Now, substitute the length and width into the area formula:

\[
243 = 3w \times w
\]

This simplifies to:

\[
243 = 3w^2
\]

Thus, the equation to find the width of the rectangle is:

\[
3w^2 = 243
\]

You can solve this equation for \( w \) to find the width.

Do you want details on how to solve this equation or have any questions?

Here are 5 related questions:
1. What is the width of the rectangle if we solve the equation \( 3w^2 = 243 \)?
2. How do you calculate the perimeter of this rectangle?
3. If the area were doubled, how would the equation change?
4. Can the width be a non-integer value in this case?
5. What if the length were 4 times the width—how would the equation change?

**Tip:** Always check units when solving real-world geometry problems to avoid mistakes.

A rectangle's length is 3 times its width, w. Its area is 243 square units. Which equation can be used to find the width of the rectangle?

This problem helps students solve for the width of a rectangle given that its length is 3 times the width and the area is 243 square units. Learn how to set up and solve the quadratic equation 3w^2 = 243, suitable for students in Grades 8-10.

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