The perimeter of a trapezium is 58 cm and sum of its non - parallel sides is 20 cm . If its no - parallel sides is 20 cm . If its areais `152 cm ^(2)` . Then the distnace between the parallel sides (in cm ) is

Options

A. `9 . 8 `
B. ` 15.2`
C. 6
D. 8

Answer

To solve the problem step by step, we will follow the information given in the question:

### Step 1: Understand the given information
We know:
- The perimeter of the trapezium is 58 cm.
- The sum of the non-parallel sides is 20 cm.
- The area of the trapezium is 152 cm².

### Step 2: Set up the equation for the perimeter
Let the lengths of the parallel sides be \( a \) and \( b \). The perimeter of a trapezium can be expressed as:
\[ \text{Perimeter} = a + b + \text{(sum of non-parallel sides)} \]
Given that the sum of the non-parallel sides is 20 cm, we can write:
\[ a + b + 20 = 58 \]
Now, we can solve for \( a + b \):
\[ a + b = 58 - 20 = 38 \quad \text{(Equation 1)} \]

### Step 3: Set up the equation for the area
The area \( A \) of a trapezium is given by the formula:
\[ A = \frac{1}{2} \times (a + b) \times h \]
Where \( h \) is the height (the distance between the parallel sides). Substituting the area and the sum of the parallel sides into the formula:
\[ 152 = \frac{1}{2} \times 38 \times h \]

### Step 4: Solve for the height \( h \)
First, simplify the equation:
\[ 152 = 19h \]
Now, divide both sides by 19 to find \( h \):
\[ h = \frac{152}{19} = 8 \text{ cm} \]

### Final Answer
The distance between the parallel sides (height) is \( \boxed{8} \) cm.

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