Two adjacent sides of a parallelogram are of length 15 cm and 18 cm. If the distance between two smaller sides is 12 cm, then the distance between two bigger sides is

Options

A. 8 cm
B. 10 cm
C. 12 cm
D. 15 cm

Answer

To solve the problem, we need to find the distance between the two longer sides of the parallelogram given the lengths of the sides and the distance between the shorter sides. Here’s how we can approach the solution step by step:

### Step 1: Understand the Problem
We have a parallelogram with two adjacent sides measuring 15 cm and 18 cm. The distance between the two shorter sides (15 cm) is given as 12 cm. We need to find the distance between the two longer sides (18 cm).

**Hint:** Visualize the parallelogram and label the sides and heights to understand the relationships.

### Step 2: Use the Area Formula
The area of a parallelogram can be calculated using the formula:
\[ \text{Area} = \text{Base} \times \text{Height} \]

We can calculate the area using both pairs of sides:
1. Using the shorter side (15 cm) as the base and the distance (height) between them (12 cm):
\[ \text{Area} = 15 \, \text{cm} \times 12 \, \text{cm} = 180 \, \text{cm}^2 \]

2. Using the longer side (18 cm) as the base and the unknown distance (let's call it \( x \)) as the height:
\[ \text{Area} = 18 \, \text{cm} \times x \]

**Hint:** Remember that the area calculated using different bases must be equal since they refer to the same parallelogram.

### Step 3: Set the Areas Equal
Since both expressions represent the area of the same parallelogram, we can set them equal to each other:
\[ 15 \times 12 = 18 \times x \]

**Hint:** This step is crucial as it allows us to solve for the unknown height \( x \).

### Step 4: Solve for \( x \)
Now we can solve the equation:
\[ 180 = 18x \]
To find \( x \), divide both sides by 18:
\[ x = \frac{180}{18} = 10 \, \text{cm} \]

**Hint:** Simplifying fractions can often lead to quicker solutions.

### Conclusion
The distance between the two longer sides of the parallelogram is \( 10 \, \text{cm} \).

**Final Answer:** 10 cm