Question

A right angled triangle PQR is such that ZPRQ = 90° and QR = 4 cm Tis a point on
QR such that PT =3 cm, and perimeter of triangle PQT = Perimeter of triangle PTR
Then, QT/TR takes the value:
a) QT/TR < 1/3
bị 1/3 < QT/TR< 1
c] QT/TR> 1
d) can't be determined
​

Answer 1

Answer:

QT/TR <1/3

IS THE ANSWER

Answer 2

Step-by-step explanation:

Given P (∆PRT) = P (∆PTQ)

=> PR + RT + PT = PT + TQ + PQ

=> PR + RT = QT + PQ

Since, PQ > PR (PQ is hypotenuse)

=> RT > QT

=> QT/TR < 1

Also, given PT = 3 so RT < 3 (PT is hypotenuse)

Since, RT + TQ = 4, when RT = 3, TQ = 1

But Since RT < 3

so 1/RT >1/3

multiply QT on both sides

QT ~ 1

∴ QT/TR > 1/3