The perimeter of a trapezium is 58 cm and sum of its non-parallel sides is 20 cm. If its area is `152cm^(2)`. Then the distance 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 use the given information about the trapezium.

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

### Step 2: Determine the sum of the parallel sides
Let the lengths of the parallel sides be AB and CD. According to the perimeter formula for a trapezium:
\[ P = AB + CD + AD + BC \]
Substituting the known values:
\[ 58 = AB + CD + 20 \]
Now, we can isolate the sum of the parallel sides:
\[ AB + CD = 58 - 20 \]
\[ AB + CD = 38 \text{ cm} \]

### Step 3: Use the area formula for the trapezium
The area (A) of a trapezium can be calculated using the formula:
\[ A = \frac{1}{2} \times (AB + CD) \times h \]
Where \( h \) is the height (distance between the parallel sides). We know:
\[ 152 = \frac{1}{2} \times (38) \times h \]

### Step 4: Simplify the area equation
Multiply both sides of the equation by 2 to eliminate the fraction:
\[ 304 = 38 \times h \]

### Step 5: Solve for the height (h)
Now, divide both sides by 38 to find the height:
\[ h = \frac{304}{38} \]
Calculating this gives:
\[ h = 8 \text{ cm} \]

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

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