Question

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Using ruler and compasses only, construct a parallelogram ABCD such that BC = 4cm, diagonal AC = 8.6cm and diagonal BD = 4.4cm. Measure the side AB.

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Answer 1

Given :

• BC = 4cm; AC = 8.6cm; BD = 6cm

To find :

• the length of AB

Solution :

Step to construct the triangle

• Construct triangle OBC such that

OB = 1/2 × BD = 1/2 × 4.4cm = 2.2cm

OC = 1/2 × AC = 1/2 × 8.6cm = 4.3cm

• Since, diagonals of ∣∣ gm bisect each other and BC=4cm
• Produce BO toD such that BO=OD=2.2cm
• Produce CO to A such that CO=OA=4.3cm
• Join AB,AD and CD Thus, ABCD is the required parallelogram.

• Measure the side AB,

AB = 5.6cm

Answer 2

Answer:

AB=5.6

Step-by-step explanation:

1. construct ∆le obc such that

ob= 1/2 * bd= 1/2* 4.4 cm = 2.2 cm

oc= 1/2 *ac= 1/ 2 *8.6 cm= 4.3 cm

( since diagonal of ll gram bisect each other) and bc= 4 cm

2. produce bo to d such that ob =od = 2.2 cm

3. produce co to a such that co= oa = 4.3 cm

4. join ab, ad and cd

5. abcd required ll gram

6. measure the side of ab = 5.6