A parallelogram ABCD has sides AB = 24 cm and AD = 16 cm. The distance between the sides AB and DC is 10 cm. Find the distance between the sides AD and BC.

Options

A. 16 cm
B. 18 cm
C. 15 cm
D. 26 cm

Answer

To solve the problem, we need to find the distance between the sides AD and BC of the parallelogram ABCD. We already have the lengths of the sides and the distance between the sides AB and DC. Let's break this down step by step.

### Step 1: Understand the Properties of a Parallelogram
In a parallelogram, opposite sides are equal and parallel. Therefore, we have:
- AB = DC = 24 cm
- AD = BC = 16 cm

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

We can use AB as the base and the distance between AB and DC as the height:
- Base (AB) = 24 cm
- Height (distance between AB and DC) = 10 cm

Now, calculate the area:
\[ \text{Area} = 24 \, \text{cm} \times 10 \, \text{cm} = 240 \, \text{cm}^2 \]

### Step 3: Use the Area to Find the Distance Between AD and BC
Now, we can use the same area to find the distance between the sides AD and BC. We will use AD as the base this time:
- Base (AD) = 16 cm
- Let the distance between AD and BC be \( h \).

Using the area formula again:
\[ \text{Area} = \text{Base} \times \text{Height} \]
\[ 240 \, \text{cm}^2 = 16 \, \text{cm} \times h \]

### Step 4: Solve for \( h \)
Now, we can solve for \( h \):
\[ h = \frac{240 \, \text{cm}^2}{16 \, \text{cm}} \]
\[ h = 15 \, \text{cm} \]

### Conclusion
The distance between the sides AD and BC is \( 15 \, \text{cm} \).

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