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What value of x,  would cause the rectangles to have the same area?



To find the value of \( x \) that would cause the two rectangles to have the same area, let's calculate the area of each rectangle and set them equal to each other.

1. **Left Rectangle**: The dimensions are \( 2 \) (height) and \( 5 + x \) (width).
   - Area of the left rectangle \( = 2 \times (5 + x) = 10 + 2x \).

2. **Right Rectangle**: The dimensions are \( x \) (width) and \( 4 \) (height).
   - Area of the right rectangle \( = x \times 4 = 4x \).

### Equation:
Set the areas equal to each other:
\[
10 + 2x = 4x
\]

Now, let's solve for \( x \).The value of \( x \) that would cause the rectangles to have the same area is \( x = 5 \).

Do you want more details or have any questions?

Here are 5 related questions you might find useful:
1. What would the areas of the rectangles be when \( x = 5 \)?
2. How do you solve equations that involve variables on both sides?
3. How does changing the dimensions affect the area of a rectangle?
4. Can this method be used to find equal areas for shapes other than rectangles?
5. What happens to the dimensions if the rectangles have different shapes but equal areas?

**Tip:** When setting up equations with variables, it's always helpful to double-check your expressions for each shape to avoid errors.

What value of x would cause the rectangles to have the same area?

Learn how to find the value of x that causes two rectangles to have the same area by setting up an equation based on their dimensions. This problem covers basic algebra and geometry concepts, suitable for students in Grades 7-9.

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