The dimensions of a photograph are 4 and 1.8 cms. If the breadth of the enlarged photo is 4.5 cm and it was enlarged proportionally then what is the new length of new photograph?

Options

A. 6
B. 5.4
C. 10
D. 9

Answer

To solve the problem step by step, we need to find the new length of the photograph after it has been enlarged proportionally.

### Step 1: Identify the original dimensions of the photograph.
The original dimensions of the photograph are:
- Length (l1) = 4 cm
- Breadth (b1) = 1.8 cm

### Step 2: Identify the new breadth of the enlarged photograph.
The new breadth (b2) of the enlarged photograph is given as:
- Breadth (b2) = 4.5 cm

### Step 3: Set up the proportion for enlargement.
Since the photograph is enlarged proportionally, we can set up the following proportion:
\[ \frac{l1}{b1} = \frac{l2}{b2} \]
Where:
- l2 = new length of the photograph (which we need to find)

### Step 4: Substitute the known values into the proportion.
Substituting the known values into the proportion gives us:
\[ \frac{4}{1.8} = \frac{l2}{4.5} \]

### Step 5: Cross-multiply to solve for l2.
Cross-multiplying gives us:
\[ 4 \cdot 4.5 = 1.8 \cdot l2 \]
Calculating the left side:
\[ 18 = 1.8 \cdot l2 \]

### Step 6: Solve for l2.
To find l2, divide both sides by 1.8:
\[ l2 = \frac{18}{1.8} \]
Calculating the division:
\[ l2 = 10 \text{ cm} \]

### Conclusion:
The new length of the enlarged photograph is **10 cm**.

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