Question

6. Using ruler and compasses construct a
parallelogram ABCD given that AB = 4 cm.
AC = 10 cm. BD = 6 cm and that AC and BD
are the diagonals. Measure BC. ​

Answer 1

Parallelogram ABCD is constructed whose one sides AB = 4 cm & Diagonals AC =10 cm & BD = 6 cm

Step-by-step explanation:

Fact to be use here is that Diagonals of a parallelogram bisect each other

Let Say AC & BD intersect at O

then AO = OC = AC/2 = 10/2 = 5 cm

BO = DO = BD/2 = 6/2 = 3cm

Draw BC=4cm.

Step 1 : Draw a Line segment AB = 4cm using ruler

Step 2 : Taking A as center draw an arc of radius = 5 cm

Step 3 : Taking B as center draw an arc of 3 cm radius , intersecting 1st arc at O

Step 4 : Join AO  & Extend till C  such that AO = OC  

Step 5 : Join BC

Step 6 : Join BO  & Extend till D  such that BO = OD  

Step 7 : Join AD

Step 8 : Join BD

on Measuring BC ≈ 7.2 cm

BC = 2√13 cm (calculated)

Answer 2

Given :

• AB = 4cm; AC = 10cm; BD = 6cm

To Find :

• the length of BC

Solution :

Steps to construct the parallelogram

• Construct triangle OAB such that

OA = 1/2 × AC = 1/2 × 10cm = 5cm

OB = 1/2 × BD = 1/2 × 6cm = 3cm

As, diagonal of parallelogram bisects each other and AB = 4cm.

• Produce AO to C such that OA=OC=5cm
• Produce BO to D such that OB=OD=3cm
• Join AD,BC and CD
• Thus, ABCD is the required parallelogram
• Measure BC which is equal to 7.2cm