Question

Construct the following quadrilateral: Rhombus $\text{BEND. BN = 5.6 cm, ED = 6.5 cm}$

Answer 1

By the properties of the Rhombus, we know that the diagonals of the rhombus are perpendicular bisector of each other.

Let's draw a rough sketch of the rhombus to get an idea of the figure

$$\begin{gathered} \text{BN = 5.4 cm} \\ \text{ED = 6.5 cm} \end{gathered}$$

Let's construct the rhombus$\text{BEND}$, using the above information -

Step 1: Draw a line segment$\text{ED = 6.5 cm}$. Take an arc of radius more than half of $\text{ED}$, and draw arc from the points $\text{D and E}$ on both sides of the line segment $\text{ED}$ which intersect each other at $\text{X and Y}$ -

Step 2: Join$\text{XY}$, which intersects line segment $\text{ED}$ at point$\text{O}$. Take an arc of radius $\text{2.8 cm}$ and draw arcs from point$\text{O}$ on a line segment$\text{XY}$, which intersect $\text{XY}$ at $\text{B and N}$ -

Step 3: Join $\text{BE, EN, ND and DB}$, to the required rhombus -

Hence, $\text{BEND}$ IS the required rhombus.