## Chapter 4 Ex.4.2 Question 1

Construct the following quadrilaterals.

(i) Quadrilateral \(LIFT\)

\({LI } =4\,\rm {cm}\)

\(IF =3\, \rm{cm}\)

\(TL=2.5\,\rm{cm}\)

\(LF=4.5\,\rm{cm}\)

\(IT =4\, \rm{cm} \)

(ii) Quadrilateral \(GOLD\)

\(OL = 7.5 \,\rm{cm}\)

\(GL = 6\,\rm{cm}\)

\(GD = 6\,\rm{cm}\)

\(LD = 5\,\rm{cm}\)

\(OD = 10 \rm \,cm\)

(iii) Rhombus \(BEND\)

\(BN = 5.6\,\rm{cm}\)

\(DE = 6.5\,\rm{cm}\)

**What is the known?**

Measurements of a Quadrilateral.

**What is unknown?**

Construction of a Quadrilateral

**Reasoning: **

As you are aware, we need five measurements to draw a quadrilateral

**Steps:**

Let us draw a rough diagram with the given measurements to find out whether it is possible to construct a quadrilateral

Based on the given information it is easy to find out that the five given measurements are of \(3\) sides and two diagonals. When measurements of \(3\) sides and two diagonals of a quadrilateral are given, we can construct a quadrilateral The construction can be done in two parts. First draw \(\Delta {{LIF}}\) and then draw \(\Delta {{LIT}}\) and then join the other side.

Let us see whether it is possible

In \(\Delta {{LIF,}}\; 4 + 3 > 4.5\) and \(4 - 3 < 4.5\)

\(4.5 + 3 > 4\) and \(4.5 - 3 < 4\)

\(4.5 + 4 > 3\) and \(4.5 - 4 < 3\)

In\( \Delta LIT,\;4 + 4 > 2.5\) and \(4 - 4 < 2.5\)

\(4 + 2.5 > 4\) and \(4 - 2.5 < 4\)

\(4 + 2.5 > 4\) and \(4 - 2.5 < 4\)

In both cases, it is possible to form triangle.

Let us construct the quadrilateral

**Step 1:** Construct Line \(LI=4 \,\rm{cm.}\) With \(L\) as center and \(4.5\,\rm{ cm}\) as radius draw an arc. With \(I\) as center and \(3\,\rm{cm}\) as radius draw an arc cutting the former one. The intersection point is \(F.\) Join \(IF\) and \(LF.\)

**Step 2:** With \(L\) as center and radius \(2.5\,\rm{cm} \) draw an arc. With \(I\) as center and \(4\,\rm{cm}\) as radius draw an arc cutting the former one at \(T.\) Join \(LT\) and \(IT.\)

**Step 3:** Join \(FT.\)

**Step 4:** \( LIFT\) is the required quadrilateral

**Related Problems**

(ii) Quadrilateral \(GOLD\)

\[\begin{align}OL&=7.5\,\rm{cm}\\GL&=6\,\rm{cm}\\GD&=6\,\rm{cm}\end{align}\]

\[\begin{align}LD&=5\,\rm{cm}\\OD&=10\,\rm{cm}\end{align}\]

(iii) Rhombus \( BEND\)

\[\begin{align}BN&=5.6\,\rm{cm} \\DE&=6.5\,\rm{cm}\end{align}\]