The perimeter of a parallelogram ABCD = 40 cm , AB = 3x cm, BC = 2x cm and CD = 2( y+1) cm . Find the values of x and y.

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the properties of a parallelogram
In a parallelogram, opposite sides are equal. Therefore, we can set up equations based on the given information.

### Step 2: Set up the equations
Given:
- Perimeter of parallelogram ABCD = 40 cm
- AB = 3x cm
- BC = 2x cm
- CD = 2(y + 1) cm = 2y + 2 cm

Since opposite sides are equal:
- AD = BC = 2x cm
- CD = AB = 3x cm

### Step 3: Write the perimeter equation
The perimeter (P) of a parallelogram is given by the formula:
\[ P = 2(AB + BC) \]
Substituting the values we have:
\[ 40 = 2(3x + 2x) \]

### Step 4: Simplify the perimeter equation
Now we simplify the equation:
\[ 40 = 2(5x) \]
\[ 40 = 10x \]

### Step 5: Solve for x
To find x, divide both sides by 10:
\[ x = \frac{40}{10} \]
\[ x = 4 \]

### Step 6: Use the value of x to find y
Now we know that AB = 3x and CD = 2y + 2. Since AB = CD:
\[ 3x = 2y + 2 \]
Substituting the value of x:
\[ 3(4) = 2y + 2 \]
\[ 12 = 2y + 2 \]

### Step 7: Solve for y
Now, isolate y:
\[ 12 - 2 = 2y \]
\[ 10 = 2y \]
\[ y = \frac{10}{2} \]
\[ y = 5 \]

### Final Answer
Thus, the values are:
- \( x = 4 \)
- \( y = 5 \)

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