A and B are two fixed points 5 cm apart and C is a point on AB such that AC in 3 cm. If the length of AC is increased by 6%, the length of CB is decreased by

Options

A. 0.06
B. 0.07
C. 0.08
D. 0.09

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the given information
We have two fixed points A and B that are 5 cm apart. Point C is on line segment AB such that AC = 3 cm. Therefore, we can find CB.

**Hint:** Identify the relationship between the lengths of AC, CB, and AB.

### Step 2: Calculate the length of CB
Since AB = 5 cm and AC = 3 cm, we can find CB using the formula:
\[ CB = AB - AC \]
\[ CB = 5 \, \text{cm} - 3 \, \text{cm} = 2 \, \text{cm} \]

**Hint:** Use subtraction to find the remaining length when one part is known.

### Step 3: Calculate the increase in length of AC
We are told that the length of AC is increased by 6%. To find the new length of AC, we first calculate 6% of 3 cm:
\[ \text{Increase} = \frac{6}{100} \times 3 \]
\[ \text{Increase} = 0.18 \, \text{cm} \]

Now, we can find the new length of AC:
\[ \text{New AC} = AC + \text{Increase} \]
\[ \text{New AC} = 3 \, \text{cm} + 0.18 \, \text{cm} = 3.18 \, \text{cm} \]

**Hint:** To find a percentage increase, multiply the original amount by the percentage expressed as a decimal.

### Step 4: Calculate the new length of CB
Now that we have the new length of AC, we can find the new length of CB:
\[ \text{New CB} = AB - \text{New AC} \]
\[ \text{New CB} = 5 \, \text{cm} - 3.18 \, \text{cm} = 1.82 \, \text{cm} \]

**Hint:** The total length remains constant; use the total length to find the new segment lengths.

### Step 5: Calculate the decrease in length of CB
To find out how much CB has decreased, we subtract the new length of CB from the original length of CB:
\[ \text{Decrease in CB} = CB - \text{New CB} \]
\[ \text{Decrease in CB} = 2 \, \text{cm} - 1.82 \, \text{cm} = 0.18 \, \text{cm} \]

**Hint:** The decrease is found by comparing the original and new lengths.

### Final Answer
The length of CB is decreased by **0.18 cm**.

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