Question

P 3. In adjoining figure 1.14 seg Ps I seg RQ seg QT I seg PR. If RQ = 6, PS = 6 and PR = 12, then find QT. R. Q S Fig. 1.14​

Answer 1

Answer:

PS⊥RQ and QT⊥PR

Also, RQ=6,PS=6 and PR=12

Using RQ as base and PS as corresponding height,

∵ Area if triangle =

2

1

×Base×Height

⇒ ΔPQR=

2

1

×RQ×PS

⇒ ΔPQR=

2

1

×6×6

⇒ ΔPQR=3×6=18 ...(i)

Now, Again using PR as base and QT as corresponding height,

Area of ΔPQR=

2

1

×PR×QT

⇒18=

2

1

×12×QT..from eq (1)

⇒18=6×QT

⇒QT×6=18⇒QT=

6

18

=3

Hence, QT=3 units