6. A piece of string is 40 cm long. What will be the length of each side if the string is used to form a square? 7. The area of a rectangular piece of cardboard is $$ 38 \mathrm{sq} . \mathrm{cm} $$ and its length is 9 cm . What is the width of the cardboard?

Question

UpStudy AI · Accepted Answer

Certainly! Let's solve each problem step by step.

---

### **Problem 6**

**A piece of string is 40 cm long. What will be the length of each side if the string is used to form a square?**

**Solution:**

1. **Understanding the Problem:**
   - A square has four equal sides.
   - The total length of the string will be the perimeter of the square.

2. **Formula for the Perimeter of a Square:**
   $$
   \text{Perimeter} = 4 \times \text{side length}
   $$

3. **Given:**
   $$
   \text{Perimeter} = 40\, \text{cm}
   $$

4. **Calculating the Side Length:**
   $$
   4 \times \text{side length} = 40\, \text{cm}
   $$
   $$
   \text{side length} = \frac{40\, \text{cm}}{4} = 10\, \text{cm}
   $$

**Answer:**  
Each side of the square will be **10 cm** long.

---

### **Problem 7**

**The area of a rectangular piece of cardboard is $$ 38\, \text{cm}^2 $$ and its length is 9 cm. What is the width of the cardboard?**

**Solution:**

1. **Understanding the Problem:**
   - The area of a rectangle is calculated as the product of its length and width.

2. **Formula for the Area of a Rectangle:**
   $$
   \text{Area} = \text{length} \times \text{width}
   $$

3. **Given:**
   $$
   \text{Area} = 38\, \text{cm}^2
   $$
   $$
   \text{length} = 9\, \text{cm}
   $$

4. **Calculating the Width:**
   $$
   38\, \text{cm}^2 = 9\, \text{cm} \times \text{width}
   $$
   $$
   \text{width} = \frac{38\, \text{cm}^2}{9\, \text{cm}} \approx 4.222\, \text{cm}
   $$

**Answer:**  
The width of the cardboard is approximately **4.222 cm**.

---

If you need the width in a fractional form, it can be expressed as:

$$
\text{width} = \frac{38}{9}\, \text{cm} \approx 4\frac{2}{9}\, \text{cm}
$$

---

Feel free to ask if you have any more questions!
**Problem 6:** Each side of the square is **10 cm**. **Problem 7:** The width of the cardboard is approximately **4.22 cm**.

6. A piece of string is 40 cm long. What will be the length of each side if the string is used to form a square? 7. The area of a rectangular piece of cardboard is \( 38 \mathrm{sq} . \mathrm{cm} \) and its length is 9 cm . What is the width of the cardboard?

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Geometry Questions