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.