The area of a trapezium -shaped field is `720 m^(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 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 distance between the two parallel sides).

Given:
- Area \( A = 720 \, m^2 \)
- Height \( h = 20 \, m \)
- One parallel side \( a = 35 \, m \)
- Let the other parallel side be \( b \).

We need to find \( b \).

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

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

### Step 2: Simplify the equation.

First, simplify the right side:

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

Calculating \( \frac{1}{2} \times 20 \):

\[ 720 = 10 \times (35 + b) \]

### Step 3: Divide both sides by 10.

\[ 72 = 35 + b \]

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

Subtract 35 from both sides:

\[ b = 72 - 35 \]

\[ b = 37 \]

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

### Final Answer:
The length of the other parallel side is \( 37 \, m \).

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