Question

Guys plz do this...as fast as u can.. emergency... I've tried but can't ...do step by step explanation...plz...​

Answer 1

Step-by-step explanation:

Let QS = ST = TR = x units

Then,

QS = x units, QT = 2x units and QR = 3x units.

Now,

(i) From ΔPQS,

PS² = PQ² + QS²

⇒ PS² = PQ² + x²

(ii) From ΔPQT,

PT² = PQ² + QT²

⇒ PT² = PQ² + (2x)²

⇒ PT² = PQ² + 4x²

(iii) From ΔPQR,

PR² = PQ² + QR²

⇒ PR² = PQ² + (3x)²

⇒ PR² = PQ² + 9x²

Now,

3PR² + 5PS² = 3(PQ² + 9x²) + 5(PQ² + x²)

                    = 3PQ² + 27x² + 5PQ² + 5x²

                   = 8PQ² + 32x²

                  = 8(PQ² + 4x²)

                 = 8PT²

Therefore,

8PT² = 3PR² + 5PS²

Hope it helps. If helped, Brainliest it!

Answer 2

Let QS = ST = TR = x units

Then,

QS = x units, QT = 2x units and QR = 3x units.

Now,

(i) From ΔPQS,

PS² = PQ² + QS²

⇒ PS² = PQ² + x²

(ii) From ΔPQT,

PT² = PQ² + QT²

⇒ PT² = PQ² + (2x)²

⇒ PT² = PQ² + 4x²

(iii) From ΔPQR,

PR² = PQ² + QR²

⇒ PR² = PQ² + (3x)²

⇒ PR² = PQ² + 9x²

Now,

3PR² + 5PS² = 3(PQ² + 9x²) + 5(PQ² + x²)

                    = 3PQ² + 27x² + 5PQ² + 5x²

                   = 8PQ² + 32x²

                  = 8(PQ² + 4x²)

                 = 8PT²

Therefore,

8PT² = 3PR² + 5PS²