The area of a trapezium-shaped field is `720m^(2)`, the distance between the two parallel sides is 20 m and the length of one of the parallel sides is 35 m. The length of the other parallel side is

Options

A. 37 m
B. 40 m
C. 35 m
D. 36 m

Answer

To find the length of the other parallel side of the trapezium-shaped field, we can use the formula for the area of a trapezium. The area \( A \) of a trapezium can be calculated using the formula:

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

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

### Given:
- Area \( A = 720 \, m^2 \)
- Distance between the parallel sides \( h = 20 \, m \)
- Length of one parallel side \( a = 35 \, m \)

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

We can rearrange the area formula to find the length of the other parallel side \( b \):

\[ 720 = \frac{1}{2} \times (35 + b) \times 20 \]

### Step 2: Simplify the equation.

Multiply both sides by 2 to eliminate the fraction:

\[ 1440 = (35 + b) \times 20 \]

### Step 3: Divide both sides by 20.

\[ \frac{1440}{20} = 35 + b \]

Calculating the left side:

\[ 72 = 35 + b \]

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

Subtract 35 from both sides:

\[ b = 72 - 35 \]

Calculating the right side:

\[ b = 37 \, m \]

### Conclusion:

The length of the other parallel side is \( 37 \, m \).

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