Question

A trapezium with $3$ equal sides and one side double the equal side can be divided into __________ equilateral triangles of _______ area.

• A. $3$
• B. Equal

Answer 1

Two triangles are said to be congruent if all the sides of a triangle are equal to all the corresponding sides of another triangle.

Step 1: In trapezium $ABCD$

Let $ABCD$is a trapezium in which

$$\begin{gathered} AD=DC=BC=a \\ AB=2a \end{gathered}$$

Now, draw medians through $D$ the vertices and $C$ on the side $AB$

$AE=EB=a$

Step 2: In trapezium $ADCE$

Now in parallelogram $ADCE$, we have

$$\begin{gathered} AD=EC=a \\ AE=CD=a \end{gathered}$$

The parallelogram has equal opposite sides

In triangle$ADE$ and $DEC,$

$$\begin{gathered} AD=EC \\ AE=CD \\ DE=BC \end{gathered}$$

Hence, the triangles $ADE$ and $DEC,$ are equilateral triangles having equal sides, which means trapezium can be divided into $3$ equilateral triangles of equal area.