CAT 2024 Question Paper | Quant Slot 1

CAT Questions

CAT 2024 Quant was dominated by Algebra followed by Arithmetic. 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 :ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of \(\triangle A D E\) is

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Video Explanation

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Explanatory Answer

In right angled triangle \(A D E, A D^2+D E^2=A E^2\)
\(\begin{array}{l}45^2+28^2=A E^2 \\ A E=\sqrt{2025+784}=\sqrt{2809}=53\end{array}\)
In-radius of a right-angled triangle \(=(a+b-h) / 2\), where "a" \(\&\) "b" are the lengths of the legs of the triangle and h is hypotenuse.
In-radius of the \(\triangle A D E=(45+28-53) / 2=10 cm\)

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The question is "ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of \(\triangle A D E\) is"

Hence, the answer is '10'

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