Here is the extracted text from your image:

1. The side of a square exceeds the side of another square by 5 cm, and the sum of the area of two squares is 325 cm². Find the side of each square.
2. There is a square of side 44 cm. Find the radius of the circle whose perimeter is equal to the perimeter of the square.

Let me solve these problems for you.

1. Solve for the sides of the squares

Let the side of the smaller square be $x$ cm.
Then the side of the larger square is $x + 5$ cm.

The area of the smaller square is $x^2$.
The area of the larger square is $(x+5)^2$.

From the problem:
$x^2 + (x+5)^2 = 325$

Expanding $(x+5)^2$:
$x^2 + x^2 + 10x + 25 = 325$
Simplify:
$2x^2 + 10x + 25 = 325$
$2x^2 + 10x - 300 = 0$
Divide through by 2:
$x^2 + 5x - 150 = 0$

Factoring the quadratic equation:
$(x+15)(x-10) = 0$
Thus, $x = -15$ (not valid as side length cannot be negative) or $x = 10$.

So, the side of the smaller square is $x = 10$ cm.
The side of the larger square is $x+5 = 15$ cm.

2. Solve for the radius of the circle

The perimeter of the square is $4 \times \text{side length} = 4 \times 44 = 176$ cm.

The circumference of the circle is equal to the perimeter of the square:
$2\pi r = 176$
$r = \frac{176}{2\pi} = \frac{88}{\pi} \approx 28.0 \, \text{cm} \, (\text{using } \pi \approx 3.14)$

Thus, the radius of the circle is approximately 28.0 cm.

Summary of Results:

1. Side of the smaller square = 10 cm; side of the larger square = 15 cm.
2. Radius of the circle = 28.0 cm.

Would you like further explanation or additional details?

5 Related Questions:

1. How do you solve quadratic equations by factoring?
2. What is the relationship between the area and side length of a square?
3. How can you derive the formula for the circumference of a circle?
4. What are alternative ways to solve quadratic equations if factoring isn't possible?
5. How do you approximate $\pi$ more accurately for real-world applications?

Tip:

For solving quadratic equations, always try factoring first. If that doesn't work, use the quadratic formula or completing the square!