UPSC CDS 1 2022 Math Paper

Given:
The diagonal of a square is 12√2cm
The area of an equilateral triangle (AT) is 64√3cm2‌‌⋯-(i)
Formula Used:
Perimeter of square =4x
Area of square =x2
Diagonal of square =√‌2.x
Where, x= side length of square
Perimeter of equilateral ∆=3a
Area of equilateral ∆=√3a2∕4
Calculation:
Let teh length of side of square be x
And the length of side of equilateral ∆ be a
According to the question
√2⋅x=12√2
⇒x=12
So, Perimeter of square =4×12=48cm‌‌− (ii)
Area of square
(AS)=122=144cm2‌‌⋯ (iii)
Again according to the question
√3a2∕4=64√3
⇒a2=256cm2
⇒a=16cm
So, Perimeter of equilateral ∆=3×16=48cm‌‌⋯-(iv)
From (ii) and (iv), we get
Perimeter of square = Perimeter of equilateral ∆
Statemetn 1 is correct And from (i) and (iii), we get
‌

AS

AT

=‌

144

64√3

⇒‌

AS

AT

=‌

3√3

4

⇒4AS=3√3AT
Statement 2 is also correct.
∴ Both the statements are correct.