Question

Rhombus PQRB is inscribed in ABC such that angle B is one of its angle. P, Q and R
lie on AB, AC and BC respectively. If AB=12 cm and BC = 6 cm, find the sides
PQ, RB of the rhombus.​

Answer 1

Answer:

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HEYA MATE HERE IS UR ANSWER

=4 cm

Step-by-step explanation:

In triangle ABC, BC is parallel to PQ.

Let side of rhombus be a cm.

Given AB = 12 cm. So AP = 12 – a

BC = 6 cm

We have AP / AB = PQ / BC

12 – a / 12 = a / 6

12 a = 72 – 6 a

18 a = 72

a = 72 / 18

a = 4 cm

❣️Hope this helps uh❣️

Answer 2

CORRECT QUESTION:

Rhombus PQRB is inscribed in △ABC such that ∠B is one of the its angle, P, Q and R lie on AB, AC and BC respectively. If AB = 12 cm and BC = 6 cm find the sides of rhombus PQRB.

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ANSWER:

Sides PQ = RB = 4 cm

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GIVEN:

• Rhombus PQRB is inscribed in △ABC

• ∠B is one of the its angle

• P, Q and R lie on AB, AC and BC

• AB = 12 cm and BC = 6 cm

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TO FIND:

• Sides of rhombus PQ,RB.

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EXPLANATION:

In a rhombus, opposite sides are parallel

Hence△ABC, PQ ∣∣ BC

By using Thales theorem

AP / AB = PQ / BC

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Let PQ = x

In a rhombus, all sides are of equal length

If PQ = x then PB = x

Substitute PB = x and AB = 12 cm in AP + PB = AB

• AP + PB = AB

• AP + x = 12

• AP = 12 - x

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Substitute AP = 12 - x, AB = 12 cm, PQ = x and BC = 6 cm in AP / AB = PQ / BC

• (12 - x) / 12 = x / 6

• (12 - x) / 2 = x

• 2x = 12 - x

• 3x = 12

• x = 4 cm

HENCE THE LENGTH OF

PQ = QR = RB = PB = 4 cm.

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NOTE: REFER ATTACHMENT FOR DIAGRAM.