now we are moving on to the topic of ratios.A 20 m cable is cut into 3 sections in the ratio 2 : 3 : 5. Find the length of each section.

To solve this problem, we will determine the length of each section of the cable based on the given ratio \(2 : 3 : 5\).

### Step 1: Understanding the Ratio
The ratio \(2 : 3 : 5\) represents the proportion of the total length that each section will occupy. Let's denote the lengths of the three sections by \(2x\), \(3x\), and \(5x\), where \(x\) is a common multiplier.

### Step 2: Set Up the Equation
The sum of the lengths of the three sections equals the total length of the cable, which is 20 meters:
\[
2x + 3x + 5x = 20
\]

### Step 3: Simplify the Equation
Combine the terms on the left side:
\[
10x = 20
\]

### Step 4: Solve for \(x\)
Divide both sides of the equation by 10 to find \(x\):
\[
x = \frac{20}{10} = 2
\]

### Step 5: Find the Length of Each Section
Now that we know \(x = 2\), we can calculate the length of each section:
- First section: \(2x = 2 \times 2 = 4\) meters
- Second section: \(3x = 3 \times 2 = 6\) meters
- Third section: \(5x = 5 \times 2 = 10\) meters

### Final Answer:
The lengths of the three sections are:
- **4 meters**
- **6 meters**
- **10 meters**

Would you like any further details or explanations?

Here are 5 related questions that you might find useful:

1. How would the lengths change if the total cable length were 30 meters instead of 20 meters?
2. What if the ratio were changed to 4:5:6? What would the lengths of the sections be?
3. Can you express the lengths of the sections as percentages of the total length?
4. How would the result differ if the ratio was 1:1:1, assuming the same total length?
5. What is the general method for dividing any total length into parts given a specific ratio?

**Tip:** When working with ratios, always remember that the sum of the parts of the ratio represents the total quantity to be divided.

Learn how to find the lengths of cable sections in the ratio 2:3:5 with a step-by-step solution. This problem covers the concept of ratio and proportion in mathematics. Suitable for students in Grades 7-9.

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