UPSC CDS 2 2020 Math Paper

Let length of one diagonal is a unit and length of another diagonal is b unit.
It is given that diagonals of a rhombus differ by 2 units
⇒ a=b+2
Perimeter of the rhombus =2√a2+b2
According to question
⇒2√a2+b2−(a+b)=6
⇒2√(b+2)2+b2 −(b+2+b)=6
⇒2√2b2+4+4b=2b+8
⇒4(2b2+4b+4) =4b2+64+32b
⇒4b2−16b−48=0
⇒b2−4b−12=0
⇒b2−6b+2b−12=0
⇒b(b−6)+2(b−6)=0
⇒(b−6)(b+2)=0
⇒b=6 or b=−2
Length of diagonal can not be negative.
Hence, Length of diagonal is 6 cm
Also, a = b +2 = 6 + 2 = 8 units
Hence, Area of rhombus =

1

2

×d1×d2=

1

2

×8×6 =24cm2