If two adjacent sides of a rectangle are `4x + 7y` and 3y - x, then find its perimeter.

Options

A. `3x+20y`
B. `x+15y`
C. `6x+ 20y`
D. `6x + y`

Answer

To find the perimeter of a rectangle when given the lengths of its adjacent sides, we can follow these steps:

### Step 1: Identify the sides of the rectangle
The two adjacent sides of the rectangle are given as:
- Length (L) = \(4x + 7y\)
- Breadth (B) = \(3y - x\)

### Step 2: Write the formula for the perimeter of a rectangle
The formula for the perimeter (P) of a rectangle is:
\[ P = 2(L + B) \]

### Step 3: Substitute the values of L and B into the formula
Substituting the values of L and B into the perimeter formula, we get:
\[ P = 2((4x + 7y) + (3y - x)) \]

### Step 4: Simplify the expression inside the parentheses
Now, we simplify the expression inside the parentheses:
\[ P = 2(4x + 7y + 3y - x) \]
Combine like terms:
\[ P = 2((4x - x) + (7y + 3y)) = 2(3x + 10y) \]

### Step 5: Multiply by 2
Now, we multiply the entire expression by 2:
\[ P = 2 \times (3x + 10y) = 6x + 20y \]

### Final Answer
Thus, the perimeter of the rectangle is:
\[ P = 6x + 20y \]

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