UPSC CDS 2 2021 Math Paper

(c) Given,Area of rhombus ABCD=336cm2Length of one of its diagonal =48cm We know, the area of rhombus
=‌

1

2

(d1×d2)
Where, d1 and d2 are the lengths of the diagonals.
Therefore, 336=‌

1

2

×(48)
× (length of other diagonal)
The length of other diagonal
=‌

336

24

=14cm
We know that, diagonals of rhombus bisect each other at right angle.
∵AO=‌

1

2

×14=7cm‌ and ‌
BO=‌

1

2

×48=24cm
∴‌ In ‌△ABO,
AB2=OA2+OB2
AB2=72+242
AB=√49+576=25cm.
‌ Length of side of rhombus ‌=25cm
‌ Perimeter of rhombus ‌=4×25cm
=100cm‌. ‌