Question

The diagonals of a rhombus differ by 2 units
and its perimeter exceeds the sum of the
diagonals by 6 units. What is the area of the
rhombus?​

Answer 1

Answer:

Let the diagonals of the rhombus be a and b

then, b−a=4 or b=(4+a)

Area of rhombus =

2

1

ab=30

a(4+a)=60

4a+a

2

=60

a

2

+4a−60=0

a=

2

−4±

16+240

=

2

−4±16

∴a=6,−10

Taking only positive value of a

Other diagonal =6+4=10cm

Thus diagonals are 6cm and 10cm