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The given image depicts a rectangle with dimensions 4 cm by 3 cm, where diagonals intersect, forming a triangle with side \( x \). The diagonals of a rectangle are equal and intersect at the center, forming right-angled triangles.

### Steps to solve for \( x \):

1. The diagonals of the rectangle act as the hypotenuse of the right-angled triangle formed, with the legs of the triangle being half of the rectangle's length and width.

   So, the legs of the right triangle are:
   - Half of the width = \( \frac{4}{2} = 2 \) cm
   - Half of the height = \( \frac{3}{2} = 1.5 \) cm

2. Use the Pythagorean theorem to find the length of the diagonal \( d \), which is the hypotenuse of the right triangle:
   \[
   d = \sqrt{(2)^2 + (1.5)^2} = \sqrt{4 + 2.25} = \sqrt{6.25} = 2.5 \, \text{cm}
   \]

3. Since the diagonals of the rectangle are equal and intersect at the center, the value of \( x \) is half the length of the diagonal:
   \[
   x = \frac{2.5}{2} = 1.25 \, \text{cm}
   \]

### The value of \( x \) is 1.25 cm.

Would you like further clarification or details?

Here are 5 questions to deepen your understanding:
1. How would the calculation change if the rectangle had different dimensions?
2. What would happen to the value of \( x \) if the rectangle became a square?
3. Can you derive the diagonal formula for any rectangle in terms of its length and width?
4. How would you calculate the area of the rectangle and the triangles formed by the diagonals?
5. Could you apply the Pythagorean theorem to a triangle where one side is not perpendicular?

**Tip:** The Pythagorean theorem is only valid for right-angled triangles, so always check the angle before applying it!

Find the value of x in the given rectangle with dimensions 4 cm by 3 cm.

Find the value of x in a rectangle with dimensions 4 cm by 3 cm. Learn how to apply the Pythagorean theorem to solve for the diagonal of the rectangle and understand right-angled triangles. Suitable for students in Grades 6-8.

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