https://file.aiquickdraw.com/mathbot/file/17373724822993zwqc6fd.jpg

Let's break down and solve the two problems shown in the image:

---

### **Problem 1:**
**The side of a square exceeds the side of another square by 5 cm, and the sum of the area of the two squares is 325 cm². Find the side of each square.**

Let the side of the smaller square be \(x\) cm.  
The side of the larger square is \(x + 5\) cm.  

The area of the smaller square = \(x^2\).  
The area of the larger square = \((x + 5)^2\).  

According to the problem,  
\[
x^2 + (x + 5)^2 = 325
\]

Expanding the equation:
\[
x^2 + (x^2 + 10x + 25) = 325
\]
\[
2x^2 + 10x + 25 = 325
\]
\[
2x^2 + 10x - 300 = 0
\]
Simplify by dividing the entire equation by 2:
\[
x^2 + 5x - 150 = 0
\]

Now solve the quadratic equation using the quadratic formula:  
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Here, \(a = 1\), \(b = 5\), and \(c = -150\).  
\[
x = \frac{-5 \pm \sqrt{5^2 - 4(1)(-150)}}{2(1)}
\]
\[
x = \frac{-5 \pm \sqrt{25 + 600}}{2}
\]
\[
x = \frac{-5 \pm \sqrt{625}}{2}
\]
\[
x = \frac{-5 \pm 25}{2}
\]

Taking the positive root:
\[
x = \frac{-5 + 25}{2} = \frac{20}{2} = 10
\]

So, the side of the smaller square is **10 cm**, and the side of the larger square is:
\[
10 + 5 = 15 \, \text{cm}.
\]

---

### **Problem 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.**

The perimeter of the square is:
\[
4 \times 44 = 176 \, \text{cm}.
\]

The perimeter of a circle is given by:
\[
2\pi r,
\]
where \(r\) is the radius of the circle.

Equating the two perimeters:
\[
2\pi r = 176
\]
\[
r = \frac{176}{2\pi} = \frac{88}{\pi}
\]

Using \(\pi \approx 3.1416\):
\[
r \approx \frac{88}{3.1416} \approx 28 \, \text{cm}.
\]

The radius of the circle is approximately **28 cm**.

---

Would you like detailed explanations or derivations of any steps? Let me know!  

### Related Questions:
1. What is the general formula for solving quadratic equations?
2. How can you verify the solution to a quadratic equation?
3. How does the formula for the perimeter of a circle relate to its radius?
4. What is the relationship between the areas of squares and circles for the same perimeter?
5. How do you approximate \(\pi\) in calculations involving circles?

### Tip:
Always double-check your results when solving quadratic equations by substituting the roots back into the original equation.

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

Learn how to solve problems involving the areas of two squares and the radius of a circle with a perimeter equal to the square's perimeter. This detailed step-by-step solution is suitable for students in Grades 7-9, covering quadratic equations and geometry.

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