# A rhombus whose diagonals are 4 cm and 6 cm in lengths. Construct the following and give justification

**Solution:**

We know that

All sides of a __rhombus__ are equal and the diagonals are perpendicular bisectors of one another

Steps of Construction

1. Construct the diagonal AC of 4 cm length

2. Considering A and C as centres and radius more than half of AC construct arcs on both sides of the line segment AC which intersect each other

3. Now cut both arcs which intersect each other at the point P and Q and join PQ

4. Let PQ intersect line segment AC at O. So PQ is the perpendicular bisector of AC

5. Now cut 3 cm length from OP and OQ, then we get B and D

6. Join AB, BC, CD and DA

7. ABCD is the required rhombus

Justification

D and B lie on the perpendicular bisector of AC

As every point on the perpendicular bisector of line segment is equidistant from end points of line segment

DA = DC and BA = BC …. (1)

∠DOC = 90°

OD = OB = 3 cm

AC is the __perpendicular bisector__ of BD

CD = CB … (2)

AB = BC = CD = DA

From equation (1) and (2)

ABCD is a rhombus.

Therefore, ABCD is a rhombus.

**✦ Try This: **Construct each of the following and give justification: A rhombus whose diagonals are 5 cm and 7 cm in lengths.

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 11

**NCERT Exemplar Class 9 Maths Exercise 11.4 Problem 5**

## A rhombus whose diagonals are 4 cm and 6 cm in lengths. Construct the following and give justification

**Summary:**

A rhombus can be defined as a special parallelogram as it fulfills the requirements of a parallelogram, i.e. a quadrilateral with two pairs of parallel sides. A rhombus whose diagonals are 4 cm and 6 cm in lengths is constructed and justified

**☛ Related Questions:**

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