The length of a rectangle is greater than twice its breadth by 4 cm if the perimeter  of the rectangle is 26 cm find its  length and breadth 

Let the length of the rectangle be \( L \) cm and the breadth be \( B \) cm.

### Step 1: Express the relationship between length and breadth
According to the problem, the length \( L \) is 4 cm more than twice the breadth \( B \). This can be written as:
\[
L = 2B + 4
\]

### Step 2: Use the perimeter formula
The perimeter \( P \) of a rectangle is given by:
\[
P = 2(L + B)
\]
The problem states that the perimeter is 26 cm, so:
\[
2(L + B) = 26
\]
Dividing both sides by 2:
\[
L + B = 13
\]

### Step 3: Substitute the expression for \( L \)
From Step 1, we know \( L = 2B + 4 \), so substitute this into \( L + B = 13 \):
\[
(2B + 4) + B = 13
\]
Simplify:
\[
3B + 4 = 13
\]
Subtract 4 from both sides:
\[
3B = 9
\]
Divide by 3:
\[
B = 3 \text{ cm}
\]

### Step 4: Find \( L \)
Now, substitute \( B = 3 \) into the equation for \( L \):
\[
L = 2(3) + 4 = 6 + 4 = 10 \text{ cm}
\]

### Final Answer:
- **Length** \( L = 10 \) cm
- **Breadth** \( B = 3 \) cm

Would you like a more detailed explanation, or do you have any questions?

Here are 5 related questions:
1. What is the area of the rectangle?
2. How would the dimensions change if the perimeter was 40 cm?
3. What if the length was 6 cm more than twice the breadth?
4. How would you calculate the diagonal of the rectangle?
5. How does the perimeter formula relate to that of a square?

**Tip:** Always check if the equation you set up correctly reflects the conditions given in the problem.

The length of a rectangle is greater than twice its breadth by 4 cm. If the perimeter of the rectangle is 26 cm, find its length and breadth.

Learn how to solve for the length and breadth of a rectangle where the length is 4 cm greater than twice the breadth, and the perimeter is 26 cm. This step-by-step solution involves key algebraic concepts such as linear equations and the perimeter formula. Suitable for Grades 6-8 students.

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