The perimeter of a trapezium is 58 cm and sum of its non-parallel sides is 20 cm. If its area is `152 cm^2`, then the distance between the parallel sides, in cms, is:

Options

A. 8
B. 9.8
C. 15.2
D. 6

Answer

To solve the problem step by step, we need to find the distance between the parallel sides of the trapezium given the perimeter, the sum of the non-parallel sides, and the area.

### Step 1: Understand the given information
- Perimeter of the trapezium (P) = 58 cm
- Sum of the non-parallel sides (a + b) = 20 cm
- Area of the trapezium (A) = 152 cm²

### Step 2: Set up the equation for the perimeter
The perimeter of a trapezium is given by the formula:
\[ P = a + b + c + d \]
where \( a \) and \( b \) are the lengths of the non-parallel sides, and \( c \) and \( d \) are the lengths of the parallel sides.

From the given information, we can express this as:
\[ 58 = 20 + (c + d) \]
This simplifies to:
\[ c + d = 58 - 20 = 38 \text{ cm} \]

### Step 3: Use the area formula for the trapezium
The area (A) of a trapezium can be calculated using the formula:
\[ A = \frac{1}{2} \times (c + d) \times h \]
where \( h \) is the height (distance between the parallel sides).

Substituting the known values into the area formula:
\[ 152 = \frac{1}{2} \times 38 \times h \]

### Step 4: Solve for the height (h)
First, simplify the equation:
\[ 152 = 19h \]
Now, solve for \( h \):
\[ h = \frac{152}{19} \]
Calculating this gives:
\[ h = 8 \text{ cm} \]

### Final Answer
The distance between the parallel sides of the trapezium is **8 cm**.

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