Question

if oq:pq=3:4 and perimeter 60cm find oq, pq,of right angled triangle opq

Answer 1

Let op =x, then using the ratio relationship we get pq =3/4x

Using pythogreas theorem to obtain oq:

x2+3/4x2=oq2

x2+9/16x2=x2(25/16)

Getting their square root :

(x2) 25/16))^1/2=5/4x

Using the given Perimeter to get the unknown :

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

12/4x=60cm

3x=60cm

x=20cm

3/4×20=15cm

op=20cm

pq=15cm

Answer 2

Let x be Common Ratio

⟹OQ=3x,PQ=4x

In △POQ

(OQ)

2

+(PQ)

2

=(PO)

2

⟹PO=5x

Since perimeter =60

⟹x=5

⟹PQ=20,

QR=24,

OP=25