The perimeter of a parallelogram is 140cm . If one of the sides is longer than the other by 10 cm, find the length of each of its sides.

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the problem
The perimeter of a parallelogram is given as 140 cm. One side is longer than the other by 10 cm. We need to find the lengths of both sides.

### Step 2: Define the variables
Let the length of the shorter side be \( x \) cm. Therefore, the length of the longer side will be \( x + 10 \) cm.

### Step 3: Write the formula for the perimeter
The formula for the perimeter \( P \) of a parallelogram is given by:
\[ P = 2 \times (\text{length} + \text{breadth}) \]
In our case, the length is \( x + 10 \) and the breadth is \( x \). Thus, we can write:
\[ P = 2 \times (x + 10 + x) \]

### Step 4: Substitute the given perimeter
We know the perimeter \( P \) is 140 cm, so we can set up the equation:
\[ 140 = 2 \times (x + 10 + x) \]

### Step 5: Simplify the equation
Simplifying the equation gives:
\[ 140 = 2 \times (2x + 10) \]
\[ 140 = 4x + 20 \]

### Step 6: Isolate the variable
To isolate \( x \), subtract 20 from both sides:
\[ 140 - 20 = 4x \]
\[ 120 = 4x \]

### Step 7: Solve for \( x \)
Now, divide both sides by 4:
\[ x = \frac{120}{4} = 30 \]

### Step 8: Find the lengths of both sides
Now that we have \( x \), we can find the lengths of both sides:
- Shorter side = \( x = 30 \) cm
- Longer side = \( x + 10 = 30 + 10 = 40 \) cm

### Final Answer
The lengths of the sides of the parallelogram are:
- Shorter side: 30 cm
- Longer side: 40 cm

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