Question

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

Answer 1

Answer:

Rhombus PQRB is inscribed in A ABC

such that B is one of its angle. P, Q and R

lie on AB, AC and BC respectively. If AB

= 12cm and BC = 6cm find the sides of

rhombus PQRB.

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.

ANSWER:

Sides PQ = RB = 4 cm

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

TO FIND:

Sides of rhombus PQ,RB.

EXPLANATION:

In a rhombus, opposite sides are parallel

Hence△ABC, PQ ∣∣ BC

By using Thales theorem

AP / AB = PQ / BC

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

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

HENCE THE LENGTH OFPQ = QR = RB = PB = 4 cm.