A farmer has a field in the shape of an isosceles trapezium whose perimeter is 215 m. One of its non parallel sides is 50m. What is the sum of its parallel sides?

Options

A. 115m
B. 60m
C. 165m
D. 135m

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the shape and given information
We have an isosceles trapezium, which means it has two parallel sides and two non-parallel sides that are equal in length. The perimeter of the trapezium is given as 215 m, and one of the non-parallel sides is 50 m.

**Hint:** Remember that in an isosceles trapezium, the non-parallel sides are equal.

### Step 2: Define the sides of the trapezium
Let's denote:
- The lengths of the two parallel sides as \( a \) and \( b \).
- The lengths of the two non-parallel sides (which are equal) as \( c \).

From the problem, we know:
- \( c = 50 \) m (the length of one non-parallel side).
- The perimeter \( P = a + b + c + c = 215 \) m.

**Hint:** The perimeter of a shape is the sum of the lengths of all its sides.

### Step 3: Write the equation for the perimeter
Substituting the known values into the perimeter equation:
\[ P = a + b + 2c \]
\[ 215 = a + b + 2(50) \]

**Hint:** Substitute the value of \( c \) into the equation.

### Step 4: Simplify the equation
Now, simplify the equation:
\[ 215 = a + b + 100 \]
Subtract 100 from both sides:
\[ a + b = 215 - 100 \]
\[ a + b = 115 \]

**Hint:** Make sure to perform the arithmetic correctly when simplifying.

### Step 5: Conclusion
The sum of the lengths of the two parallel sides \( a \) and \( b \) is 115 m.

**Final Answer:** The sum of the parallel sides is **115 m**.