CAT 2021 Question Paper | Quant Slot 2

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

Video Explanation

Explanatory Answer

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, \( a ^ { 2 } + b ^ { 2 } \) = 25.
\( ( a + b ) ^ { 2 } = a ^ { 2 } + b ^ { 2 } + 2 a b \)
\( ( a + b ) ^ { 2 } = 25 + 2 ( 6 ) = 37 \)
\( a + b = \sqrt { 37 } \) → eq(1)
\( ( a - b ) ^ { 2 } = a ^ { 2 } + b ^ { 2 } - 2 a b \)
\( ( a - b ) ^ { 2 } = 25 - 2 ( 6 ) = 13 \) 
\( a - b = \sqrt { 13 } \) → eq(2)
By solving eq(1) & (2) we get
Long diagonal = 2a = \( \sqrt { 37 } + \sqrt { 13 } \)

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 '\(\sqrt{37}+\sqrt{13}\)'

Choice C is the correct answer.

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