Question

M and N are mid points of sides AD and BC in the trapezium ABCD. AB = 6.5 cm, MN = 8 cm.

∴ DC = ........

Options

• 8.5 cm

• 7.5 cm

• 9 cm

• 9.5 cm

Answer 1

9.5 cm

Explanation:

In the trapezium ABCD,

We are given the following information: 

• AB = 6.5 cm, 
• MN = 8 cm, where M and N are midpoints of sides AD and BC, respectively.

We need to find the length of DC, which is the length of the other parallel side of the trapezium.

Step 1: Use the Midline Theorem

The Midline Theorem for a trapezium states that the line segment joining the midpoints of the non-parallel sides (in this case, MN) is parallel to both the parallel sides AB and DC and its length is the average of the lengths of the two parallel sides:

`MN = (AB + DC)/2`

Step 2: Set up the equation

We are given:

• AB = 6.5 cm
• MN = 8 cm

Using the Midline Theorem:

`8 = (6.5 + DC)/2`

Step 3: Solve for DC

Multiply both sides by 2 to eliminate the fraction:

16 = 6.5 + DC

Now, solve for DC:

DC = 16 – 6.5 = 9.5 cm