The area of a trapezium is 279 sq. cm and the distance between its two parallel sides is 18 cm. If one of its parallel sides is longer than the other side by 5 cm, find the lengths of its parallel sides.

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the problem
We are given the area of a trapezium, the distance between its parallel sides, and the relationship between the lengths of the parallel sides. We need to find the lengths of these parallel sides.

### Step 2: Define the variables
Let:
- \( CD = x \) (the length of the shorter parallel side)
- \( AB = x + 5 \) (the length of the longer parallel side)

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

### Step 4: Substitute the known values into the formula
We know:
- Area \( A = 279 \, \text{sq. cm} \)
- Height \( h = 18 \, \text{cm} \)

Substituting these values into the area formula gives:
\[ 279 = \frac{1}{2} \times (x + (x + 5)) \times 18 \]

### Step 5: Simplify the equation
First, simplify the expression inside the parentheses:
\[ 279 = \frac{1}{2} \times (2x + 5) \times 18 \]
Now, simplify further:
\[ 279 = 9 \times (2x + 5) \]

### Step 6: Solve for \( x \)
Now, divide both sides by 9:
\[ \frac{279}{9} = 2x + 5 \]
Calculating \( \frac{279}{9} \):
\[ 31 = 2x + 5 \]
Now, subtract 5 from both sides:
\[ 31 - 5 = 2x \]
\[ 26 = 2x \]
Now, divide by 2:
\[ x = 13 \]

### Step 7: Find the lengths of the parallel sides
Now that we have \( x \):
- \( CD = x = 13 \, \text{cm} \)
- \( AB = x + 5 = 13 + 5 = 18 \, \text{cm} \)

### Final Answer
The lengths of the parallel sides are:
- \( CD = 13 \, \text{cm} \)
- \( AB = 18 \, \text{cm} \)

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