Question

Construct the following quadrilateral: Quadrilateral $\text{GOLD}$. $\text{OL = 7.5 cm, GL = 6 cm, GD = 6 cm, LD = 5 cm, OD = 10 cm}$

Answer 1

Let's draw a rough sketch of a quadrilateral$\text{GOLD}$, to get an idea about the parallelogram -

$$\begin{gathered} \text{GL = 6 cm} \\ \text{OD = 10 cm} \\ \text{DL = 5 cm} \\ \text{GD = 6 cm} \\ \text{OL = 7.5 cm} \end{gathered}$$

Let's construct the quadrilateral$\text{GOLD}$ using the information given in the question -

Step 1: Draw a line segment$\text{DL = 5 cm}$,

Then take an arc of radius $\text{6 cm}$ on the compass & cut an arc from the point$\text{D \& L}$, which bisect each other at point$\text{G}$ -

Step 2: Join $\text{GD \& GL}$,

Then take an arc of radius $\text{10 cm}$ on the compass & cut an arc from point$\text{D}$, then change the radius to $\text{7.5 cm}$ and cut another arc from point$\text{L}$ which intersect each other at point$O$ and then join $\text{DO and OL}$

Step 3: Join $\text{OG}$ to get the required quadrilateral -

Hence, $\text{GOLD}$is the required quadrilateral.