CAT 2022 Question Paper | Quant Slot 1

CAT Questions

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 19 : All the vertices of a rectangle lie on a circle of radius \(R\). If the perimeter of the rectangle is \(P\), then the area of the rectangle is

---

---

Video Explanation

---

---

Explanatory Answer

Let the dimensions of the rectangle inscribed in the circle be a and b.
We are being asked to express the Area of the rectangle in terms of Perimeter and Radius.
Area of the rectangle = a * b
Perimeter, P = 2(a + b)
a + b = \( \frac { P } { 2 } \)
\( ( a + b ) ^ { 2 } = \frac { P ^ { 2 } } { 4 } \)
\( a ^ { 2 } + b ^ { 2 } + 2 a b = \frac { P ^ { 2 } } { 4 } \)
Since the vertices of the rectangle subtend right angle on the circle,
\( a ^ { 2 } + b ^ { 2 } = ( 2 R ) ^ { 2 } = 4 R ^ { 2 } \)
\( a ^ { 2 } + b ^ { 2 } + 2 a b = \frac { P ^ { 2 } } { 4 } \)
\( 4 R ^ { 2 } + 2 a b = \frac { P ^ { 2 } } { 4 } \)
\( a b = \frac { P ^ { 2 } } { 8 } - 2 R ^ { 2 } \)
Area of the rectangle = ab = \( \frac { p ^ { 2 } } { 8 } - 2 R ^ { 2 } \)

---

The question is " All the vertices of a rectangle lie on a circle of radius \(R\). If the perimeter of the rectangle is \(P\), then the area of the rectangle is "

Hence, the answer is '\(\frac{P^2}{8}-2 R^2\)'

Choice B is the correct answer.

Verbal Ability for CAT | CAT Reading Comprehension

Verbal Ability for CAT| CAT Para Jumble

Verbal Ability for CAT | CAT Sentence Elimination

Verbal Ability for CAT | CAT Paragraph Completion

Verbal Ability for CAT | CAT Critical Reasoning

Verbal Ability for CAT | CAT Word Usage

Verbal Ability for CAT| CAT Para Summary

Verbal Ability for CAT | CAT Text Completion

Verbal Ability for CAT | CAT Sentence Correction