Question

ABC be right angle triangle right angled at A,P is any point on AB such that AP:PB =4:3 ,PQ||AC ,QS perpendicular to CP then find (¡) PQ:AC (¡¡) In triangle ARC , calculate the length of AR

Answer 1

Answer:

PQ:AC = 3:7, AR= 14 cms

Step-by-step explanation:

1) AP : PB = 4 : 3

So, my basic proportionality theorem

AP/PB = CQ/QB

Therefore CQ/QB = 4/3

BQ/BC = 3/7 ...(1)

Angle PQB = Angle ACB

Angle QPB = Angle CAB

Triangle PBQ ~ Triangle ABC

PQ/AC = BQ/BC

From (1)

PQ/AC = 3:7

(2) Missing Information in Question:- Angle ARC = 90, QS = 6cm

Angle ARC = Angle QSP

Angle ARC = Angle SPQ--Alternate Angles

Triangle ARC ~ Triangle QSP

AR/QS = AC/PQ

AR/QS  = 7/3

Given  QS = 6 cms

AR = 14 cm