# 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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Let’s consider the length of the longer and shorter diagonal of the rhombus to be ‘2a’ and ‘2b’ respectively.

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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