a square has the same area as a rectangle with sides of length 4 centimeters and 25 centimeters. what is the length of the square

To find the length of the square, we need to determine the area of the rectangle and then use that value to calculate the side length of the square.

### Step 1: Calculate the area of the rectangle.
The area of a rectangle is given by the formula:

\[
\text{Area of rectangle} = \text{length} \times \text{width}
\]

Given that the rectangle has sides of length 4 cm and 25 cm, the area is:

\[
\text{Area of rectangle} = 4 \, \text{cm} \times 25 \, \text{cm} = 100 \, \text{cm}^2
\]

### Step 2: Set the area of the square equal to the area of the rectangle.
Since the square has the same area as the rectangle, the area of the square is also 100 cm². The area of a square is given by:

\[
\text{Area of square} = (\text{side length})^2
\]

### Step 3: Solve for the side length of the square.
Let the side length of the square be \( s \). So, we have:

\[
s^2 = 100
\]

Taking the square root of both sides:

\[
s = \sqrt{100} = 10 \, \text{cm}
\]

### Conclusion:
The length of the side of the square is **10 centimeters**.

Would you like further details or have any questions?

Here are some related questions for practice:
1. What is the perimeter of the square with side length 10 cm?
2. How would the side length of the square change if the rectangle had sides 5 cm and 25 cm?
3. If the area of the square were 144 cm², what would be the side length?
4. What is the diagonal length of the square with a side length of 10 cm?
5. How can you express the relationship between the side of a square and its area algebraically?

**Tip:** The area of a square grows as the square of its side length, so doubling the side length results in four times the area!

A square has the same area as a rectangle with sides of length 4 centimeters and 25 centimeters. What is the length of the square?

Learn how to find the side length of a square that has the same area as a rectangle with sides of 4 cm and 25 cm. This geometry problem involves calculating the area of the rectangle and using square roots to determine the side length of the square. Suitable for students in Grades 6-8.

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