# CAT Practice : Coordinate Geometry

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Geometry - Triangles

## Basic Geometry

Q.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, ${\frac{QT}{TR}} > 2$ takes the value.
1. $\frac{QT}{TR} < \frac{1}{3}$
2. $\frac{1}{3} < \frac{QT}{TR} < 1$
3. $\frac{QT}{TR} > 1$
4. can’t be determined

Choice (B). $\frac{1}{3} < \frac{QT}{TR} < 1$

## Detailed Solution

In the figure,

Given P (∆PRT) = P (∆PTQ)
=) PR + RT + PT = PT + TQ + PQ
=) PR + RT = QT + PQ
Since, PQ > PR (PQ is hypotenuse)
=) RT > OT
=)$\frac{QT}{TR} > 1$
Also, given PT = 3 so RT $< 3$ (PT is hypotenuse)
Since, RT+ TQ = 4, when RT = 3, TQ = 1
But Since RT $< 3$
$\frac{QT}{TR} > \frac{1}{3}$

Correct Answer: (B) = $\frac{1}{3} < \frac{QT}{TR} < 1$

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Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.