Question

OQ:PQ=3:4and perimeterof tiangle POQ=60cm. Find PQ QR AND OP

Answer 1

Some part of the question is missing. The triangle given is a right angled triangle. Having this as base we can solve it by the following :

Let the side PQ = x

OQ : x = 3 : 4

=> OQ = 3x / 4

We know that,

OQ² + PQ² = OP²

X² + ( 3 X / 4 )² = OP²

x² + 9x² / 16 = OP²

Taking LCM we get,

16 x² + 9 x² / 16 = OP²

25x² / 16 = OP²

=> OP = √ ( 25x² / 16 ) = 5x / 4

=> Perimeter = x + 3x / 4 + 5x / 4 = 60 cm

Taking LCM we get,

4x + 3x + 5x / 4 = 60

=> 12 x = 60 *4

=> 12 x = 240

=> x = 240 / 12 = 20

PQ = 20 units

OQ = 3X / 4 = 3 * 20 / 4 = 60 / 4 = 15 units

OP = 5X / 4 = 5 * 20 / 4 = 100 / 4 = 25 units.

Hence measures are :

PQ = 20 ; OQ = 15 ; OP = 25 units.