The area of a trapezium is `352 cm^(2)` and the distance between its parallel sides is 16 cm. If one of the parallel sides is of length 25 cm, find the length of the other.

Answer

To solve the problem step by step, we will use the formula for the area of a trapezium. The area \( A \) of a trapezium can be calculated using the formula:

\[ A = \frac{1}{2} \times (a + b) \times h \]

where:
- \( a \) and \( b \) are the lengths of the parallel sides,
- \( h \) is the distance between the parallel sides.

### Step 1: Identify the known values
We know:
- Area \( A = 352 \, \text{cm}^2 \)
- Distance between parallel sides \( h = 16 \, \text{cm} \)
- One parallel side \( a = 25 \, \text{cm} \)
- Let the length of the other parallel side be \( b = x \).

### Step 2: Substitute the known values into the area formula
Using the area formula, we can substitute the known values:

\[ 352 = \frac{1}{2} \times (25 + x) \times 16 \]

### Step 3: Simplify the equation
First, simplify the right side of the equation:

\[ 352 = \frac{1}{2} \times (25 + x) \times 16 \]

Calculating \( \frac{1}{2} \times 16 \):

\[ 352 = 8 \times (25 + x) \]

### Step 4: Expand the equation
Now, distribute \( 8 \):

\[ 352 = 200 + 8x \]

### Step 5: Isolate \( x \)
To find \( x \), we need to isolate it on one side of the equation. First, subtract \( 200 \) from both sides:

\[ 352 - 200 = 8x \]

This simplifies to:

\[ 152 = 8x \]

### Step 6: Solve for \( x \)
Now, divide both sides by \( 8 \):

\[ x = \frac{152}{8} \]

Calculating the division:

\[ x = 19 \]

### Step 7: State the final answer
The length of the other parallel side \( b \) is:

\[ b = 19 \, \text{cm} \]

### Summary
The length of the other parallel side of the trapezium is \( 19 \, \text{cm} \).

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