The length of a rectangular playground is 9 m more than twice its breadth. If the perimeter of the ground is 90m, then find the length and the breadth of the playground.

Answer

To solve the problem step by step, we will follow the information given in the question and use algebraic expressions to find the length and breadth of the rectangular playground.

### Step 1: Define the variables
Let the breadth of the playground be \( b \) meters. According to the question, the length \( l \) of the playground is 9 meters more than twice its breadth. We can express this relationship as:
\[ l = 2b + 9 \]

### Step 2: Write the formula for the perimeter
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2(l + b) \]
We know from the question that the perimeter is 90 meters, so we can set up the equation:
\[ 2(l + b) = 90 \]

### Step 3: Substitute the expression for length into the perimeter equation
Now, we will substitute \( l \) from Step 1 into the perimeter equation:
\[ 2((2b + 9) + b) = 90 \]

### Step 4: Simplify the equation
Now, let's simplify the equation:
\[ 2(2b + 9 + b) = 90 \]
This simplifies to:
\[ 2(3b + 9) = 90 \]

### Step 5: Divide both sides by 2
To simplify further, divide both sides of the equation by 2:
\[ 3b + 9 = 45 \]

### Step 6: Isolate the variable
Now, we will isolate \( b \) by subtracting 9 from both sides:
\[ 3b = 45 - 9 \]
\[ 3b = 36 \]

### Step 7: Solve for breadth
Now, divide both sides by 3 to find \( b \):
\[ b = \frac{36}{3} \]
\[ b = 12 \text{ meters} \]

### Step 8: Find the length
Now that we have the breadth, we can find the length using the expression from Step 1:
\[ l = 2b + 9 \]
Substituting \( b = 12 \):
\[ l = 2(12) + 9 \]
\[ l = 24 + 9 \]
\[ l = 33 \text{ meters} \]

### Final Answer
The length of the playground is 33 meters and the breadth is 12 meters.

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