CAT 2021 Question Paper | Quant Slot 2

CAT Previous Year Paper | CAT Quant Questions | Question 9

CAT 2021 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 9 : If a rhombus has area 12 sq cm and side length 5 cm, then the length, in cm, of its longer diagonal is

  1. \\frac{\sqrt{37} + \sqrt{13}}{2})
  2. \\frac{\sqrt{13} + \sqrt{12}}{2})
  3. √(37) + √(13)
  4. √(13) + √(12)

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Explanatory Answer

Let’s consider the length of the longer and shorter diagonal of the rhombus to be ‘2a’ and ‘2b’ respectively.
Rhombus with sides 5 units
The area of the rhombus = 12 sq cm
\\frac{1}{2}) x 2a x 2b = 12 sq cm.
ab = 6.
The side of the rhombus = 5 cm.
So, a2 + b2 = 25.
(a + b)2 = a2 + b2 + 2ab
(a + b)2 = 25 + 2(6) = 37
a + b = √(37) → eq(1)
(a - b)2 = a2 + b2 - 2ab
(a - b)2 = 25 - 2(6) = 13 
a - b = √(13) → eq(2)
By solving eq(1) & (2) we get
Long diagonal = 2a = √(37) + √(13)


The question is " If a rhombus has area 12 sq cm and side length 5 cm, then the length, in cm, of its longer diagonal is "

Hence, the answer is '√(37) + √(13)'

Choice C is the correct answer.

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