Question

in the adjoining figure, PQR is a right triangle right angled at Q and QS perpendicular to PR. If PQ = 4 cm and PS = 2 cm, find QS, RS and QR​

Answer 1

Answer:

QS=2√3 cm

RS=6 cm

QR=4√3 cm

Step-by-step explanation:

PQ²=QS²+PS²

4²=QS²+2²

16=QS²+4

16-4=12=QS²

QS=√12=2√3cm

Let ∠ QPR=x

Therefore ∠PRQ=90-x

As ΔQSR is a right angled triangle,∠SQR=90-x

∠PQR=90

∠PQS=90-x

So by AAA ΔPQS is similar to ΔQRS

PQ/QR=QS/RS=PS/QS

QR=PQ*QS/PS

QR=4*2√3/2

QR=4√3 cm

RS=QS*QS/PS

RS =2√3*2√3/2

RS = 6 cm