Question

in triangle pqr 90 degree qg =√5,pg=3 ifg is centroid then find qr​

Answer 1

Answer:

Centroid divides each median in the ratio of 1:2

(i)Consider the median RK. KG and RG are divided in the ratio 1:2

⇒

RG

KG

​

=

2

1

​

We know KG=2 cm

⇒

RG

2

​

=

2

1

​

Cross multiply

⇒RG=4 cm

(ii) KR=KG+RG

KG=2 cm and RG=4 cm

∴KR=4+2=6 cm

(iii)Consider the median PL. PG and GL are divided in the ratio 1:2

⇒

PG

GL

​

=

2

1

​

We know PG=4.6 cm

⇒

4.6

GL

​

=

2

1

​

Cross multiply

⇒GL=2.3 cm

(iv) PL=PG+GL

PG=4.6 cm and GL=2.3 cm

∴PL=4.6+2.3=6.9 cm

(v) MQ is divided in such a way that it should form a ratio of 1:2

MQ=9 cm

∴MG:GQ is 1:2

If 9 has to be divided in a ratio of 1:2 t it will be 3 and 6

Step-by-step explanation: