Question

in triangle PQR ; angle PQR is 90°, point T is the midpoint of side QR prove that PRsquare =4PT square-3PQ​

Answer 1

Step-by-step explanation:

As per Pythagorean theorem

PT2=PQ2+QT2....(in triangle QPT)

⇒QT2=PT2−PQ2

And PR2=PQ2+QR2 ( in the triangle APR and given T is the mide point QR then QR=2QT) put value 

⇒PR2=PQ2+(2QT)2

⇒PR2=PQ2+4QT2

⇒PR2=PQ2+4(PT2−PQ2)

=PQ2+4PT2−4PQ2

⇒PR2=4PT2−3PQ2.

Answer 2

Answer:

As per Pythagorean theorem

PT 2 =PQ 2 +QT 2 ....(in triangle QPT)

⇒QT 2=PT 2−PQ 2

And PR 2 =PQ 2+QR 2( in the triangle APR and given T is the mide point QR then QR=2QT) put value

⇒PR

2=PQ 2 +(2QT) 2

⇒PR 2 =PQ 2+4QT 2

⇒PR 2 =PQ 2 +4(PT 2 −PQ 2)

=PQ 2 +4PT2−4PQ2

⇒PR 2 =4PT 2−3PQ 2.

Step-by-step explanation: