CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

The question is from the topic triangles. It is about a right angle triangle and a point on the adjacent side which divides the triangle into two. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. We have to find the possible ratio of two sides.

Question 41: A right angled triangle PQR is such that ∠PRQ = 90° and QR = 4 cm T is a point on QR such that PT = 3 cm, and perimeter of triangle PQT = Perimeter of triangle PTR Then, QT/TR takes the value:

1. QT/TR < 1/3
2. 1/3 < QT/TR < 1
3. QT/TR > 1
4. can’t be determined

Explanatory Answer

Method of solving this CAT Question from Triangles: Knowing the properties of right angle triangle would help.

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
∴ QT/TR > 1/3

The question is "QT/TR takes the value"

Hence, the answer is 1/3 < QT/TR < 1.

Choice B is the correct answer.