Question

The points A and B represent Three (3) and Five (5), respectively, on a number line. BC is drawn equal to AB such that Angle ABC = 120°. An arc is drawn equal to AC, with A as centre, which intersects the number line at D. What point is represented by D?




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Answer 1

Answer:

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Step-by-step explanation:

Clearly, ABCQ and ARBC are parallelograms.

∴BC=AQ and BC=AR

⇒AQ=AR

⇒A is the mid-point of QR.

Similarly, B and C are the mid-points of PR and PQ respectively.

∴AB=

2

1

PQ,BC=

2

1

QR and CA=

2

1

PR

⇒PQ=2AB,QR=2BC and PR=2CA

⇒PQ+QR+RP=2(AB+BC+CA)

⇒ Perimeter of ΔPQR=2 (Perimeter of ΔABC)

solution

Answer 2

Answer:

Clearly, ABCQ and ARBC are parallelograms.

∴BC=AQ and BC=AR

⇒AQ=AR

⇒A is the mid-point of QR.

Similarly, B and C are the mid-points of PR and PQ respectively.

∴AB=

2

1

PQ,BC=

2

1

QR and CA=

2

1

PR

⇒PQ=2AB,QR=2BC and PR=2CA

⇒PQ+QR+RP=2(AB+BC+CA)

⇒ Perimeter of ΔPQR=2 (Perimeter of ΔABC)