## Chapter 4 Ex.4.5 Question 1

Draw the following:

1. A square \(READ\) with \(RE = 5.1\,\rm{cm.}\)

2. A rhombus whose diagonals are \(5.2\,\rm{cm}\) and \(6.4\,\rm{cm}\) long.

3. A rectangle with adjacent sides of lengths \(5\,\rm{cm}\) and \(4\,\rm{cm.}\)

4. A parallelogram \(OKAY\) where \(OK = 5.5\,\rm{cm} \) and \(KA = 4.2\,\rm{cm.}\) Is it unique?

**What is the known?**

Diagonals of a Rhombus.

**What is unknown?**

Construction of a Rhombus

**Reasoning: **

We need five measurements to draw a unique quadrilateral.

But we also know that diagonals of rhombus bisect each other at right angles and all sides of rhombus are equal. We can use this information to construct the rhombus.

**Steps:**

**Step 1:** Draw a line segment \(AB=6.4\,\rm{cm.}\)

**Step 2:** Draw perpendicular bisector of \(AB\) meeting \(AB\) at \(O.\)

**Step 3:** \(5.2\,\rm{cm}\) divided by \(2 = 2.6 \,\rm{cm.}\) Measure \(2.6\,\rm{cm}\) from \(O\) on either side of \(AB\) on perpendicular bisector and mark them as \(C\) and \(D.\)

**Step 4:** Join \(AC, AD, BC\) and \(BD.\)

**Step 5:** \(ABCD\) is the required rhombus.

**Related Problems:**

(1) The square \(READ\) with \(RE=5.1\,\rm{cm}\)

**Hint:** All sides of square are equal, and angles are at right angles.

(2) A rectangle with adjacent sides of lengths \(5\,\rm{cm}\) and \(4\,\rm{cm.}\)

**Hint:** Opposite sides of rectangle are equal and parallel, and angles are at right angles.

(3) A parallelogram \(OKAY\) where \(OK=5.5\,\rm{cm}\) and \(KA=4.2\,\rm{cm.}\)

**Hint:** Opposite sides of a parallelogram are parallel and equal. Using this information, parallelogram can be constructed with a convenient angle.