A 5100 sq. cm trapezium has the perpendicular distance between the two parallel sides is 60 cm.
If one of the parallel sides be 40 cm then, find the length of the other parallel side.

Answer

To find the length of the other parallel side of the trapezium, we can use the formula for the area of a trapezium. The area \( A \) of a trapezium is given by:

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

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

Given:
- Area \( A = 5100 \, \text{sq. cm} \)
- Height \( h = 60 \, \text{cm} \)
- One parallel side \( a = 40 \, \text{cm} \)
- Let the other parallel side be \( b \).

### Step 1: Substitute the known values into the area formula.

\[ 5100 = \frac{1}{2} \times (40 + b) \times 60 \]

### Step 2: Simplify the equation.

First, calculate \( \frac{1}{2} \times 60 \):

\[ \frac{1}{2} \times 60 = 30 \]

Now substitute this back into the equation:

\[ 5100 = 30 \times (40 + b) \]

### Step 3: Divide both sides by 30 to isolate the term with \( b \).

\[ \frac{5100}{30} = 40 + b \]

Calculating \( \frac{5100}{30} \):

\[ 170 = 40 + b \]

### Step 4: Solve for \( b \).

Subtract 40 from both sides:

\[ b = 170 - 40 \]

Calculating this gives:

\[ b = 130 \, \text{cm} \]

### Conclusion:

The length of the other parallel side is \( 130 \, \text{cm} \).

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