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Standard X

Mathematics

Basic Proportionality Theorem

Rhombus PQR...

Question

Rhombus $P Q R B$ is inscribed in $△ A B C$ such that $∠ B$ is one of the its angle, $P$ , $Q$ and $R$ lie on $A B$ , $A C$ and $B C$ respectively. If $A B = 12 cm$ and $B C = 6 cm$ find the sides of rhombus $P Q R B$ .

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Solution

In $△ A B C, P Q | | B C$ ......... ( $∵$ In a rhombus, opposite sides are parallel)
$∴ \frac{A P}{A B} = \frac{P Q}{B C}$ ......... (Using Corollary of Thales theorem)
$⟹ \frac{12 - x}{12} = \frac{x}{6}$
$⟹ 12 x = 72 - 6 x$
$⟹ 18 x = 72$
$∴ x = 4 c m$
The sides of the rhombus is $4$ cm each.

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Similar questions

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△

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∠

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Q. A rhombus is inscribed in triangle ABC in such a way that one of its vertices is A and two its sides lie along AB and AC where AC

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In Fig., a circle inscribed in triangle ABC touches its sides AB,BC and AC at points D,E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the lengths of AD, BE and CF.

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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.

In △ABC,PQ||BC ......... (∵ In a rhombus, opposite sides are parallel)∴APAB=PQBC ......... (Using Corollary of Thales theorem)⟹12−x12=x6⟹12x=72−6x⟹18x=72∴x=4 cmThe sides of the rhombus is 4 cm each.

Rhombus $P Q R B$ is inscribed in $△ A B C$ such that $∠ B$ is one of the its angle, $P$ , $Q$ and $R$ lie on $A B$ , $A C$ and $B C$ respectively. If $A B = 12 cm$ and $B C = 6 cm$ find the sides of rhombus $P Q R B$ .