CAT 2019 Question Paper | Quants Slot 1

CAT Questions

CAT Geometry question that appears in the Quantitative Aptitude section of the CAT Exam broadly tests an aspirant on the concepts - Triangles, Circles, Quadrliaterals, Polygons & mixture of the above mentioned concepts. In CAT Exam, one can generally expect to get 4~6 questions from CAT Geometry. CAT Geometry is an important topic with lots of weightage in the CAT Exam. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score.

Question 27 : If the rectangular faces of a brick have their diagonals in the ratio 3 : 2 \\sqrt{3}) : \\sqrt{15}), then the ratio of the length of the shortest edge of the brick to that of its longest edge is

1. 1 : \\sqrt{3})
2. 2 : \\sqrt{5})
3. \\sqrt{2}) :\\sqrt{3})
4. \\sqrt{3}) : 2

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Video Explanation

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Explanatory Answer

From the given data, we know
l² + b² = 9k -------- (1)
b² + h² = 12k ------- (2)
l² + h² = 15k -------- (3)
Adding (1) , (2) and (3) we get
2(l² + b² + h²) = 36 k
l² + b² + h² = 18k -----(4)
Subtracting (1), (2) , (3) from (4) we get
h² = 9k
l² = 6k
b² = 3k
Thus, ratio of shortest edge to longest edge = = 1:

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The question is "If the rectangular faces of a brick have their diagonals in the ratio 3 : 2 \\sqrt{3}) : \\sqrt{15}), then the ratio of the length of the shortest edge of the brick to that of its longest edge is "

Hence, the answer is 1 : \\sqrt{3})

Choice A is the correct answer.