Find the area of a rectangle whose length is 5 m more than 4 times its breadth, and its perimeter is 60cm.

Answer

To find the area of the rectangle whose length is 5 m more than 4 times its breadth and whose perimeter is 60 cm, we can follow these steps:

### Step 1: Define the variables
Let the breadth of the rectangle be \( b \) cm. According to the problem, the length \( l \) can be expressed as:
\[ l = 4b + 5 \]

### Step 2: Use the perimeter formula
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2(l + b) \]
We know the perimeter is 60 cm, so we can set up the equation:
\[ 2(l + b) = 60 \]

### Step 3: Simplify the perimeter equation
Dividing both sides of the equation by 2 gives:
\[ l + b = 30 \]

### Step 4: Substitute the expression for length
Now, substitute the expression for \( l \) from Step 1 into the equation from Step 3:
\[ (4b + 5) + b = 30 \]

### Step 5: Combine like terms
Combine the terms involving \( b \):
\[ 5b + 5 = 30 \]

### Step 6: Solve for breadth
Subtract 5 from both sides:
\[ 5b = 25 \]
Now, divide by 5:
\[ b = 5 \text{ cm} \]

### Step 7: Find the length
Now that we have the breadth, we can find the length using the expression from Step 1:
\[ l = 4b + 5 = 4(5) + 5 = 20 + 5 = 25 \text{ cm} \]

### Step 8: Calculate the area
Finally, we can find the area \( A \) of the rectangle using the formula:
\[ A = l \times b \]
Substituting the values we found:
\[ A = 25 \times 5 = 125 \text{ cm}^2 \]

### Final Answer
The area of the rectangle is \( 125 \text{ cm}^2 \).