Question

@ In a trapezium PQRS, PQ || SR. The diagonals PR and QS intersect at O. If OP = 3 cm, OR = 2 cm and OS = 4 cm, then the length of side OQ is:
(a) 2 cm
(b) 4 cm
(c) 6 cm
(d) 8 cm ​

Answer 1

Answer:

B) 4 cm

Step-by-step explanation:

⇒

⇒ RS

⇒ RSPQ

⇒ RSPQ

⇒ RSPQ =

⇒ RSPQ = 3

⇒ RSPQ = 32

⇒ RSPQ = 32

⇒ RSPQ = 32

⇒ RSPQ = 32 In △PQR and △RXS

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)Also, ∠RSX=∠PQX (alternate angles)

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)Also, ∠RSX=∠PQX (alternate angles)∴△PQR≅△RXS by AA similarity theorem.

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)Also, ∠RSX=∠PQX (alternate angles)∴△PQR≅△RXS by AA similarity theorem.Hence,

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)Also, ∠RSX=∠PQX (alternate angles)∴△PQR≅△RXS by AA similarity theorem.Hence, ar(△RXS)

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)Also, ∠RSX=∠PQX (alternate angles)∴△PQR≅△RXS by AA similarity theorem.Hence, ar(△RXS)ar(△PQR)

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)Also, ∠RSX=∠PQX (alternate angles)∴△PQR≅△RXS by AA similarity theorem.Hence, ar(△RXS)ar(△PQR)

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)Also, ∠RSX=∠PQX (alternate angles)∴△PQR≅△RXS by AA similarity theorem.Hence, ar(△RXS)ar(△PQR) =(

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)Also, ∠RSX=∠PQX (alternate angles)∴△PQR≅△RXS by AA similarity theorem.Hence, ar(△RXS)ar(△PQR) =( 3

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)Also, ∠RSX=∠PQX (alternate angles)∴△PQR≅△RXS by AA similarity theorem.Hence, ar(△RXS)ar(△PQR) =( 32

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)Also, ∠RSX=∠PQX (alternate angles)∴△PQR≅△RXS by AA similarity theorem.Hence, ar(△RXS)ar(△PQR) =( 32

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)Also, ∠RSX=∠PQX (alternate angles)∴△PQR≅△RXS by AA similarity theorem.Hence, ar(△RXS)ar(△PQR) =( 32 )

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)Also, ∠RSX=∠PQX (alternate angles)∴△PQR≅△RXS by AA similarity theorem.Hence, ar(△RXS)ar(△PQR) =( 32 ) 2

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)Also, ∠RSX=∠PQX (alternate angles)∴△PQR≅△RXS by AA similarity theorem.Hence, ar(△RXS)ar(△PQR) =( 32 ) 2

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)Also, ∠RSX=∠PQX (alternate angles)∴△PQR≅△RXS by AA similarity theorem.Hence, ar(△RXS)ar(△PQR) =( 32 ) 2 =

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)Also, ∠RSX=∠PQX (alternate angles)∴△PQR≅△RXS by AA similarity theorem.Hence, ar(△RXS)ar(△PQR) =( 32 ) 2 = 9

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)Also, ∠RSX=∠PQX (alternate angles)∴△PQR≅△RXS by AA similarity theorem.Hence, ar(△RXS)ar(△PQR) =( 32 ) 2 = 94

⇒ RSPQ = 32 In △PQR and △RXS∠SRX=∠QPX (alternate angles)Also, ∠RSX=∠PQX (alternate angles)∴△PQR≅△RXS by AA similarity theorem.Hence, ar(△RXS)ar(△PQR) =( 32 ) 2 = 94

Answer 2

Answer:

c) 6 cm

Step-by-step explanation:

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