The length and the breadth of a rectangle are in the ratio 3:2 if its perimeter is 1 m 40 cm. find its dimensions.

Options

A. 24cm , 16cm
B. 84m , 56m
C. 90cm , 50cm
D. None of these

Answer

To find the dimensions of the rectangle given that the length and breadth are in the ratio 3:2 and the perimeter is 1 meter 40 cm, follow these steps:

### Step 1: Understand the Ratio
The length (L) and breadth (B) of the rectangle are in the ratio 3:2. We can express this as:
- Length (L) = 3x
- Breadth (B) = 2x

### Step 2: Convert the Perimeter to Centimeters
The perimeter of the rectangle is given as 1 meter 40 centimeters.
1 meter = 100 centimeters, so:
- Total Perimeter = 100 cm + 40 cm = 140 cm

### Step 3: Use the Perimeter Formula
The formula for the perimeter (P) of a rectangle is:
\[ P = 2(L + B) \]
Substituting the expressions for L and B:
\[ 140 = 2(3x + 2x) \]

### Step 4: Simplify the Equation
Combine the terms inside the parentheses:
\[ 140 = 2(5x) \]
Now simplify:
\[ 140 = 10x \]

### Step 5: Solve for x
To find the value of x, divide both sides by 10:
\[ x = \frac{140}{10} = 14 \]

### Step 6: Calculate Length and Breadth
Now that we have the value of x, we can find the length and breadth:
- Length (L) = 3x = 3 * 14 = 42 cm
- Breadth (B) = 2x = 2 * 14 = 28 cm

### Step 7: State the Dimensions
The dimensions of the rectangle are:
- Length = 42 cm
- Breadth = 28 cm