The length of a rectangle is three times its width and its perimeter 56m. The length is

Options

A. `7` m
B. `14` m
C. `21` m
D. `28` m

Answer

To solve the problem step by step, we will define the variables, set up the equations based on the given information, and then solve for the length of the rectangle.

### Step-by-Step Solution:

1. **Define the Variables**:
Let the width of the rectangle be \( B \) meters. According to the problem, the length \( L \) of the rectangle is three times its width. Therefore, we can express the length as:
\[ L = 3B \]

**Hint**: Start by defining the variables based on the relationships given in the problem.

2. **Write the Perimeter Equation**:
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2L + 2B \]
According to the problem, the perimeter is 56 meters. Therefore, we can write:
\[ 2L + 2B = 56 \]

**Hint**: Remember that the perimeter is the sum of all sides of the rectangle.

3. **Simplify the Perimeter Equation**:
We can factor out the 2 from the perimeter equation:
\[ 2(L + B) = 56 \]
Dividing both sides by 2 gives us:
\[ L + B = 28 \]

**Hint**: Simplifying equations can make it easier to work with them.

4. **Substitute the Length in the Perimeter Equation**:
Now, we will substitute the expression for \( L \) from step 1 into the equation we derived in step 3:
\[ 3B + B = 28 \]
This simplifies to:
\[ 4B = 28 \]

**Hint**: Use substitution to replace variables with known expressions.

5. **Solve for the Width**:
Now, we can solve for \( B \) by dividing both sides by 4:
\[ B = \frac{28}{4} = 7 \]

**Hint**: Isolate the variable to find its value.

6. **Find the Length**:
Now that we have the width \( B \), we can find the length \( L \) using the equation from step 1:
\[ L = 3B = 3 \times 7 = 21 \]

**Hint**: Substitute back to find the other variable once you have one of them.

### Final Answer:
The length of the rectangle is \( 21 \) meters.