Area of a trapezium is `1050 cm^(2) `. One of its parallel sides is 50 cm and the distance betweeen the parallel sides is 30 cm . Find the length of the other parallel side ( in cm) .

Options

A. 24
B. 20
C. 15
D. 26

Answer

To find the length of the other parallel side of the trapezium, we can use the formula for the area of a trapezium:

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

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

Given:
- Area = \( 1050 \, \text{cm}^2 \)
- One parallel side \( a = 50 \, \text{cm} \)
- Height \( h = 30 \, \text{cm} \)
- The other parallel side \( b = x \) (which we need to find).

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

\[ 1050 = \frac{1}{2} \times (50 + x) \times 30 \]

### Step 2: Simplify the equation.

First, multiply both sides by 2 to eliminate the fraction:

\[ 2100 = (50 + x) \times 30 \]

Next, divide both sides by 30:

\[ 70 = 50 + x \]

### Step 3: Solve for \( x \).

Subtract 50 from both sides:

\[ 70 - 50 = x \]

\[ x = 20 \]

### Conclusion

The length of the other parallel side is \( 20 \, \text{cm} \).

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