Question

In the given figure PQ || RS || BC. If RS = 4 cm, PQ = 3 cm, then BC is equal to ​

Answer 1

Answer:

BC = 12/7 OR 1.71

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Step-by-step explanation:

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Answer 2

Given :- In the given figure PQ || RS || BC. If RS = 4 cm, PQ = 3 cm .

To Find :- BC = ?

Solution :-

In ∆PCB and ∆PSR we have,

→ ∠PCB = ∠PSR { since RS || CB , corresponding angles are equal in measure . }

→ ∠CBP = ∠SRP { since RS || CB , corresponding angles are equal in measure . }

So,

→ ∆PCB ~ ∆PSR { By AA similarity. }

then,

→ PB/PR = CB/SR

→ PB/PR = CB/4

→ PB = (CB/4)PR ---------- Eqn.(1)

Similarly,

In ∆RCB and ∆RQP we have,

→ ∠RCB = ∠RQP { since QP || CB , corresponding angles are equal in measure . }

→ ∠RBC = ∠RPQ { since QP || CB , corresponding angles are equal in measure . }

So,

→ ∆RCB ~ ∆RQP { By AA similarity. }

then,

→ RB/RP = CB/QP

→ RB/RP = CB/3

→ RB = (CB/3)RP

→ RB = (CB/3)PR ---------- Eqn.(2)

adding Eqn.(1) and Eqn.(2) we get,

→ PB + RB = {(CB/4)PR} + {(CB/3)PR}

→ PB + BR = PR[(CB/4) + (CB/3)]

→ PR = PR[(CB/4) + (CB/3)]

→ 1 = (CB/4) + (CB/3)

→ 1 = (3CB + 4CB)/12

→ 12 = 7CB

→ CB = (12/7)

→ BC = (12/7) cm (Ans.)

Shortcut :-

When three lines are parallel to each other ,

→ 1/BC = 1/RS + 1/PQ

→ 1/BC = 1/4 + 1/3

→ 1/BC = (3 + 4)/12

→ 1/BC = (7/12)

→ BC = (12/7) (Ans.)

Hence, Length of BC is equal to (12/7) cm .

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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