Question

In figure OQ : PQ equal to 3 : 4 and perimeter of triangle POQ = 60 cm. Determine PQ QR and OP.
plz answer it fast ⚡

Answer 1

let the common ration between OQ and PQ be x then OQ = 3x and PQ = 4x

given that : perimeter of POQ = 60 cm

=> OP + OQ+ PQ = 60 cm

=> OP + 3x + 4x = 60 => OP + 7x = 60

=> OP = 60 - 7x --- ( i )

Also OQ is perpendicular to PQ since PQ is the tangent.

=> POQ is a right angle triangle , right angle at Q

=> then by pythagoras theorem , we must have

OP^2 = PQ^2 + OQ^2 = ( 4x ) ^2 + ( 3x ) ^2

= 16 x^2 + 9x^2 = 25 x^2

taking square root both sides gives ,

OP = 5x

60 - 7x = 5x using equation ( i )

=> 60 = 12x => x = 5

Thus

OQ = 3x = 3 × 5 = 15 cm

PQ = 4x = 4 × 5 = 20 cm

OP = 5x = 5 × 5 = 25 cm