Question

Solve this.........​

Answer 1

Answer:

Let,QS=x

QS=ST=TR=x

QT=2x

QR=3x

 In ΔPQT, ∠Q=90°

PT²=PQ²+QT²

     =PQ²+4x²  -------------- 1

In ΔPQR, ∠Q=90°

PR²=PQ²+QR²

     =PQ²+9x²

In ΔPQS, ∠Q=90°

PS²=PQ²+QS²

     =PQ²+x²

From eq.1

8PT²=8PQ²+32x²--------------------- eq.2

[by multiplying eq.1 by 8]

3PR²+5PS²=3(PQ²+9x²)+5(PQ²+x²)

                 =3PQ²+27x²+5PQ²+5x²

                 =8PQ²+32x²

                 =8(PQ²+4x²)

                 =8PT²       [from eq.2]

I HOPE ITS HELPFUL