Question

In the given figure, if PR=12cm,QR=6 cm and PL=8 cm, then QM is:

answer given in answer sheet is 4cm I want step wise solution.​

Answer 1

Answer:

akkajakakkakakakkasjan

Answer 2

Answer

Option (c) is corrmt

Given that PL=8cm

PR=12cm

QR=6cm

Now, In right-angled triangle PLR

Using Pythagoras theorem,

⇒PR

2

=PL

2

+LR

2

⇒LR

2

=144−64

⇒=

80

=4

5

cm

LR=LQ+QR

⇒LQ=LR−QR=(4

5

)cm

Now area of triangle PLR

A=

2

1

×(4

5

)×8

=16

5

cm

2

Now, area of triangle PLQ

A=

2

1

×(4

5

)×8

=(16

5

−24)cm

2

Hence, area of triangle PLR = Area on triangle PLQ + Area of triangle PQR

So, area of triangle PLR − Area on triangle PLQ = Area of triangle PQR

⇒16

5

−(16

5

−24),

⇒ Area of triangle PQR =24cm

2

⇒

2

1

PR×QM=24

⇒

2

1

×12×QM=24

∴QM=4cm