Question

In the given figure, OQ: PQ = 3:4 and perimeter of $△POQ=60cm$. Determine PQ, QR and OP.

Answer 1

Consider a $△POQ$

then by phythagoras theorem

if $x=1$

$(1+x{)}^2+(3x{)}^2=O{P}^2$

for $x=1$

$OP=5$ Hence $OQ:PQ:OP=3:4:5$

is perimeter of $△POQ=60cm$

then $3x+4x+5x=60$

$12x=60$

$x=5cm$

Hence $PQ=4x=4\times 5=20cm$

$QR=2OQ=2\times \left(3x\right)=2\times 3\times 5$

$=30cm$

$OP=5x=5\times 5=25cm$