A rectangle is having 15 cm as its length and `150 cm^2` as its area then area is increased to `1 1/3` times the original area by increasing only its length its new perimeter is :

Options

A. 50cm
B. 60cm
C. 70cm
D. 80cm

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Identify the given values
- Length of the rectangle (L) = 15 cm
- Area of the rectangle (A) = 150 cm²

### Step 2: Calculate the breadth (B) of the rectangle
The area of a rectangle is given by the formula:
\[ A = L \times B \]
Substituting the known values:
\[ 150 = 15 \times B \]
To find B, we rearrange the equation:
\[ B = \frac{150}{15} = 10 \text{ cm} \]

### Step 3: Calculate the new area
The area is increased to \( \frac{4}{3} \) times the original area:
\[ \text{New Area} = A \times \frac{4}{3} = 150 \times \frac{4}{3} = 200 \text{ cm}^2 \]

### Step 4: Set up the equation for the new length
Let the new length be \( L' \). The breadth remains the same (B = 10 cm). Thus, we can express the new area as:
\[ \text{New Area} = L' \times B \]
Substituting the known values:
\[ 200 = L' \times 10 \]
To find \( L' \), we rearrange the equation:
\[ L' = \frac{200}{10} = 20 \text{ cm} \]

### Step 5: Calculate the new perimeter
The perimeter (P) of a rectangle is given by the formula:
\[ P = 2(L + B) \]
Substituting the new length and breadth:
\[ P = 2(20 + 10) = 2 \times 30 = 60 \text{ cm} \]

### Final Answer
The new perimeter of the rectangle is **60 cm**.

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